In social psychology , the fundamentalattributionerror also known as correspondence bias or attribution .... The fundamentalattributionerror is most visible when people explain the behavior of others. It does ... , 1 24. ref Ross argued in a popular paper that the fundamentalattributionerror forms the conceptual ... by the fundamentalattributionerror. ref name JonesHarris67 Subjects read pro and anti Fidel Castro ... accepted explanation for the fundamentalattributionerror. Here are several ... by situational factors, we still commit the fundamentalattributionerror. ref name JonesHarris67 ... creates the fundamentalattributionerror. It also explains that people commit to fundamentalattribution ... have been found effective in reducing the effect of the fundamentalattributionerror Taking ... still prone to the fundamentalattributionerror. Cultural differences in the error Previous research has shown that cultural differences exist in the susceptibility of making fundamentalattribution ... than contextual details. Fundamentalattributionerror vs. Correspondence bias The fundamentalattributionerror is commonly used interchangeably with correspondence bias sometimes called correspondence ... argue that the fundamentalattributionerror should be considered as the tendency to make dispositional ... Association. ref ref Krull, D.S. 2001 . On partitioning the fundamentalattributionerror Dispositionalism ... to those of fundamentalattributionerror. While the latter has been found to be more prevalent ..., S., & Zhao, X. 1999 . The fundamentalattributionerror Correspondence bias in individualist and collectivist ... FundamentalAttributionError Category Cognitive biases Category Attitude attribution Category ... Daniel Gilbert , have begun using the term correspondence bias for the fundamentalattribution ... bias Actor observer bias Attributional bias False consensus effect Group attributionerror Just world phenomenon List of cognitive biases Locus of control Ultimate attributionerror References ... more details
. Belmont, CA. Wadsworth ref . The ultimate attributionerror is different from the fundamentalattributionerror in that it is used to describe entire groups of people, whereas the fundamentalattributionerror has to do with dispositional attribution s that apply only to an individual. Studies Demonstrating the Ultimate AttributionError The ultimate attributionerror was demonstrated in 1976 ..., CA. Wadsworth ref . See also Portal Psychology Fundamentalattributionerror Actor observer ...The ultimate attributionerror is a term in Social Psychology which refers to a bias people commonly have towards members of an Outgroup sociology outgroup . Specifically, they view negative acts committed ... that ultimate attributionerror is more likely to occur when there are negative associations with members ... and attribution if intergroup violence Testing the lower limits of stereotyping of Blacks. Journal of Personality and Social Psychology, 83, 75 93. Pettigrew, T.F. 1979 . The ultimate attributionerror ... 1979 . The Ultimate AttributionError Extending Allport s Cognitive Analysis of Prejudice. Personality ... members as exceptions to normal behavior. The term is a variation on another common cognitive error, the fundamentalattributionerror . Ultimate AttributionError is attributing behaviors of entire groups to their stereotypes. In Psychology, the Ultimate AttributionError is considered one of the roots of prejudice. cite Ultimate AttributionError The ultimate attributionerror is a cognitive error committed by prejudiced people in which negative behaviors are attributed to the personality ... on judgments of the ingroup as a group. Pettigrew, 1979 ref Pettigrew, T.F. 1979 . The ultimate attributionerror Extending Allport s cognitive analysis of prejudice. Personality and Social Psychology ... who are dealing with specific situations the best they can. Conversely, people who commit this error ... and attribution if intergroup violence Testing the lower limits of stereotyping of Blacks. Journal ... more details
The group attributionerror is a group serving bias group serving , attributional bias identical to the fundamentalattributionerror except that it occurs between different group sociology groups rather than different individuals. Group members are more likely to attribute the decisions of their own group to its decision rules, while they tend to attribute the decisions of another group to its members attitude. The group attributionerror was first reported by Scott Allison and David Messick. Compare to the outgroup homogeneity bias . See also Portal Psychology div style column count 2 moz column count 2 webkit column count 2 Fundamentalattributionerror Ingroup bias Attribution theory List of cognitive biases div References http dx.doi.org 10.1016 0022 1031 85 90025 3 Allison, S. T. & Messick, D. M. 1985 . The group attributionerror. Journal of Experimental Social Psychology 21 , 563 579 Category Cognitive biases Category Attitude attribution Psychology stub ... more details
Wiktionary Attribution may refer to Something, such as a quality or characteristic, that is related to a particular possessor an attribute. Attribution copyright , concept in copyright law requiring an author to be credited Attribution psychology , concept in psychology whereby people attribute traits and causes to things they observe Performance attribution , technique in quantitative finance for explaining the active performance of a portfolio Journalism sourcing or attribution , journalistic practice of attributing information to its source disambig fr Attribution ru ... more details
, and shatters his peace. ref name The Wire E53 cite episode title Not for Attribution episodelink Not for Attribution ... title The Wire episode guide episode 53 Not for Attribution accessdate 2008 01 22 publisher ... more details
Wiktionarypar fundamentalFundamental may refer to Foundation of reality . Fundamental frequency , as in music or phonetics, often referred to as simply a fundamental . Fundamentalism , the belief in, and usually the strict adherence to, the simplistic or fundamental ideas based on faith of a system of thought. The Fundamentals , a set of books important to Christian fundamentalism Any of a number of fundamental theorem s identified in mathematics, such as The fundamental theorem of algebra , a theorem regarding the factorization of polynomials. The fundamental theorem of arithmetic , a theorem regarding prime factorization. Fundamental analysis , a method that uses financial and economic analysis to predict the movement of security prices such as bond prices, but more commonly stock prices. In music Fundamental Bonnie Raitt album Fundamental Pet Shop Boys album Fundamental Puya album Fun Da Mental , a rap group. disambig cs Fundament ln es Fundamental gl Fundamental id Fundamental it Fundamental nl Fundamental ... more details
106 108 ref Types of attribution Explanatory attribution Predictive attribution Interpersonal attribution Bias and errors in attributions Fundamentalattributionerror ref Ross, 1977 ref A tendency to overestimate ... for the fundamentalattributionerror. ref Jones, E. E., & Nisbett, R. E. 1971 . The actor and the observer ... of the actor. Dispositional attributions ref Pettigrew, 1979 ref Error in attribution involves attributions ... attributionerror. Self serving attributions Self serving attributions are explanations for one ...wikify date August 2010 Attribution is a concept in social psychology referring to how individuals explain causes of events, other s behavior, and their own behavior. Causes of attribution Fritz Heider ... the person to predict and understand the events that they observe and experience. As such, attribution ... . When an internal attribution is made, the cause of the given behavior is assigned to the individual s personality, attitudes, character or disposition. When an external attribution is made ... . These two types of attribution lead to very different perceptions of the individual engaging ... the role of situational factors. One plausible reason for this error relates to the perceptual ... . ref Lerner, 1980 ref Defensive attributions are one type of self serving attribution they involve .... Optimism bias Unrealistic optimism is a form of defensive attribution in which people think that positive ... ref Type A, B personality Attribution theories Common sense psychology Fritz Heider Correspondent ... by reviewing the context of behavior. Covariation model of attribution Harold Kelley Harold Kelley ... variation Model of Attribution looks to three main types of information from which to make an attribution ... situations. From these three sources of information observers make attribution decisions on the individual s behavior as either internal or external. ref Kelley, Attribution theory in social psychology. Levine, Nebraska Symposium on Motivation ref Three dimensional model of attribution Bernard ... more details
other uses The word error entails different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word error is wandering or straying . Unlike an illusion, an error ... else. Human behavior Image Napoleons retreat from moscow.jpg right thumbnail One error and its ... by Adolph Northen in the 19th century One reference differentiates between error and mistake as follows quote An error is a deviation from accuracy or correctness. A mistake is an error caused by a fault ... on my interpretation of what the signs meant, that would be an error. The first time it would be an error ... pas can be labels for certain instances of this kind of error. More serious departures from social norms ... forms should and should not be used. See also Error analysis . Image PrintingError.jpg thumb 400px ... that can culminate in stuttering. Medicine See medical error for a description of error in medicine ... in statistics error or residual is not a mistake but rather a difference between a computed, estimated ... error . In science and engineering in general an error is defined as a difference between ... is the basis of operation for many types of Control system s, in which error is defined as the difference ... heating system the operation of the heating equipment is controlled by the difference the error ... s, machine s and system s and in such a way as to mitigate or preferably avoid the effects of error ... active. Other errors in engineered systems can arise due to human error , which includes cognitive bias . Human factors engineering is often applied to designs in an attempt to minimize this type of error by making systems more forgiving or error tolerant . In computational mechanics , when solving a system such as Ax b there is a distinction between the error &mdash the inaccuracy ... being steered cybernetics can be seen as the most general approach to error and its correction for the achievement ... Gordon Pask held that the error that drives a servomechanism can be seen as a difference between ... more details
File Cc by.svg thumb 120px Creative Commons license symbol for attribution. Attribution in copyright law, is the requirement to acknowledge or credit the author of a work which is used or appears in another work. Attribution is required by most copyright and copyleft licenses, such as the GNU Free Documentation License and Creative Commons licenses. ref Creative Commons, http wiki.creativecommons.org FAQ FAQ ref Attribution is often considered the most basic of requirements made by a license, as it allows an author to accumulate a positive reputation that partially repays their work and prevents others from claiming fraudulently to have produced the work. It is widely regarded as a sign of decency and respect to acknowledge the creator by giving him her credit for the work. See also Acknowledgment creative arts Credit creative arts References Reflist law term stub DEFAULTSORT Attribution Copyright Category Copyright law ar fr Droit de paternit pl Atrybucja sztuka ru ... more details
Orphan date October 2010 See Attribution of recent climate change Climate attribution is a scientific process for establishing the principal causes or physical explanation for observed climate conditions and phenomena. This includes attribution of the causes for observed climate variations that may not be unusual in a statistical sense but for which great public interest exists because they produce profound societal impacts. Climate attribution is most frequently associated with the process of explaining a detected change. ref name noaa def cite web url http www.esrl.noaa.gov psd csi whatis title NOAA Climate Attribution What is Attribution? work U.S. Department of Commerce, National Oceanic and Atmospheric Administration Earth System Research Laboratory, Physical Sciences Division publisher NOAA accessdate 18 October 2010 ref Mechanisms There are numerous mechanisms that may produce climate variations or change including external forcing, anthropogenic forcing, and internal mechanisms. External forcing contains both natural and anthropogenic sources such as solar variability and volcanic eruptions. Anthropogenic forcing stem are from changing concentrations of greenhouse gases and aerosol s, and land cover use produced by human activities. Internal mechanisms within the climate system can also produce climate variations through processes that are due primarily to interactions within ... variability. ref name noaa def Attribution According to the IPCC Third Assessment Report , the attribution ... combination of forcings. For attribution to be established, the relationship between the observed climate .... ref name noaa def References Reflist Source attribution cite web url http www.esrl.noaa.gov psd csi whatis title NOAA Climate Attribution What is Attribution? work U.S. Department of Commerce, National ... publisher NOAA External links http www.esrl.noaa.gov psd csi NOAA climate attribution http www.esrl.noaa.gov psd outreach resources handouts attribution final.pdf Climate Attribution , Earth System ... more details
Performance Attribution or Investment Performance Attribution is a set of techniques that performance ... is actively managed. Different kinds of performance attribution provide different ways of explaining the active return. Attribution analysis attempts to distinguish which of the two factors ... of 2.40 . This leaves an active return of 2.20 . The task of performance attribution is to explain the decisions ... paradigm for performance attribution, there are two different kinds of decision that the portfolio ... the benchmark return for equities was only 3 . The attribution analysis dissects the value added into three ..., and the equities sector also outperformed its benchmark. The three attribution terms asset allocation ... fudge factors . More modern and enhanced versions of decision attribution analysis askew the economically ... controllable decision. Decision attribution also needs to address the combined effect of multiple periods ... assets but duration decisions are only made for the fixed income assets. The most robust attribution models precisely address all of these aspects of decision attribution without residuals. Furthermore ... attribution system must always be interpreted in parallel to a precisely commensurate risk attribution analysis. History In 1972, A Working Group of the Society of Investment Analysts UK published ... the key concept in performance attribution, that active performance can be analysed by comparing ... paper introduced the key elements of modern performance attribution notional portfolios, asset ... on performance attribution for example Spaulding2003 Spaulding 2003 . It is commonly believed that Gary ... to Brinson Fachler attribution pp. 177 180. and Brinson Hood Beebower attribution pp. 29 51 . Geometric attribution The most common approach to performance attribution found in sources such as Brinson1985 Brinson et al. 1985 and Carino Carino 1999 can be described as arithmetic attribution . It is arithmetic ... attribution would explain 11 of value added. In Europe and the UK, another approach known ... more details
The fallacy of a false attribution occurs when an advocate appeals to an irrelevant, unqualified, unidentified, biased or fabricated source in support of an argument. A contextomy is a type of false attribution. A more deceptive and difficult to detect version of a false attribution is where a fraudulent advocate goes so far as to fabricate a source, such as creating a fake website, in order to support a claim. For example, the Levitt Institute was a fake organisation created in 2009 solely for the purposes of successfully fooling the Australia n media into reporting that Sydney was Australia s most na ve city. ref name Deception Detection Deficiency http www.abc.net.au mediawatch transcripts s2698835.htm Deception Detection Deficiency , Media Watch. ref A particular case of misattribution is the Matthew effect sociology Matthew effect a quotation is often attributed to someone more famous than the real author. This leads the quotation to be more famous, but the real author to be forgotten see also obliteration by incorporation . ref cite journal doi 10.1063 1.1768652 title Could Feynman Have Said This? year 2004 author Mermin, N. David journal Physics Today volume 57 pages 10 ref References Reflist External links http www.fallacyfiles.org quotcont.html Quoting Out of Context Fallacy Files. http www.scribd.com doc 8009498 HUMBUG eBook by Jef Clark and Theo Clark Humbug The skeptic s field guide to spotting fallacies in thinking textbook on fallacies. False Attribution p56 . Informal Fallacy Category Logical fallacies ... more details
Orphan date February 2009 Nuclear attribution is the process of tracing the origin of nuclear material that has been used in a nuclear explosion . ref cite news author David Sanger and Thom Shanker title U.S. Debates Deterrence for Nuclear Terrorism publisher New York Times date 7 May 2007 url http www.nytimes.com 2007 05 08 washington 08nuke.html accessdate 2008 04 29 ref The problem is not necessarily a straightforward one, for it may be possible to obtain Precursor chemistry nuclear precursors through the Underground economy black market , and therefore relatively anonymously. References reflist Category Nuclear warfare Category Forensic techniques nuclear stub forensics stub ... more details
A Question of Attribution is a 1991 television play written by Alan Bennett and commissioned by the BBC . Directed by John Schlesinger , it starred James Fox as Anthony Blunt and Prunella Scales as Elizabeth II of the United Kingdom Queen Elizabeth II . The play is based on Anthony Blunt s role in the Cambridge Spy Ring and, as Surveyor of the Queen s Pictures , personal art advisor to Queen Elizabeth II. It portrays his interrogation by MI5 officers, his work researching and restoring art, and his relationship with the Queen. Bennett described the piece as an inquiry in which the circumstances are imaginary but the pictures are real http www.screenonline.org.uk tv id 986784 . The New York Times called it a razor sharp psychological melodrama . While supervising the restoration of a dual portrait attributed to Titian , Blunt discovers a further three figures that had been painted over. As Blunt s public exposure as a spy in 1979 draws near the play suggests that he has been made a scapegoat to protect others in the security service. One of the main themes is over whether or not the Queen knew that Blunt was a former Soviet spy. In one scene Blunt discovers that a painting in the Queen s collection is a fake. When she is told this, the Queen discusses the nature of fakes and secrets. After she has left and an aide asks what they were talking about, Blunt replies I was talking about art. I m not sure that she was. The play was also performed in 1988 with An Englishman Abroad as one act plays under the title Single Spies . The play won the 1992 BAFTA TV award for Best Single Drama, and Prunella Scales was nominated for Best Actress. See also Cambridge Spies , a 2003 BBC TV play about the Cambridge Ring, and how Blunt came to be a Soviet agent. References imdb title id 0105204 http www.screenonline.org.uk tv id 986784 screenonline review , retrieved 17 January 2006 http www.bbc.co.uk ... , retrieved 17 January 2006 John Schlesinger DEFAULTSORT Question of Attribution,A Category BBC television ... more details
The fundamental plane may refer to The fundamental plane spherical coordinates fundamental plane which divides a spherical coordinate system. The fundamental plane elliptical galaxies fundamental plane which shows an empirical relationship between mean surface brightness, velocity dispersion and effective radius of an elliptical galaxy. disambig ... more details
The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming ... ref For example, the fundamental theorem of calculus gives the relationship between differential .... The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory . The mathematical literature sometimes refers to the fundamental ... in and of itself. The fundamental lemma of a field is often, but not always, the same as the fundamental theorem of that field. Fundamental lemmas Fundamental lemma of calculus of variations Fundamental lemma of Langlands and Shelstad Fundamental lemma of sieve theory Feinstein s fundamental lemma information theory Fundamental lemma of interpolation theory numerical analysis Fundamental theorems of mathematical topics Fundamental theorem of algebra Fundamental theorem of arithmetic Fundamental theorem of calculus Fundamental theorem of curves Fundamental theorem of cyclic groups Fundamental theorem of surfaces Fundamental theorem of finitely generated abelian groups Fundamental theorem of Galois theory Fundamental theorem on homomorphisms Fundamental theorem of linear algebra Fundamental theorem of projective geometry Fundamental theorem of Riemannian geometry Fundamental theorem of vector analysis Fundamental theorem of linear programming Non mathematical fundamental theorems There are also a number of fundamental theorems more aptly a series of rule of thumb not directly related to mathematics Fundamental theorem of arbitrage free pricing Fisher s fundamental theorem of natural selection Fundamental theorems of welfare economics Thermodynamic potentials The fundamental equations Fundamental equations of thermodynamics Fundamental theorem of poker See also List of theorems Notes reflist Fundamental theorems Category Mathematical theorems Category Fundamental theorems es Teorema fundamental fr Th or me fondamental hi ka nl Hoofdstelling ... more details
The mathematical term fundamental sequence can refer to In analysis, Cauchy sequence . In discrete mathematics and computer science, Unary coding . In set theory, a fundamental sequence ordinals fundamental sequence for an ordinal is a sequence of ordinals approaching the limit ordinal from below. disambig ... more details
Fundamental law s may refer to Organic law , in particular, Constitution , in particular, The Russian Constitution of 1906 . The German Grundgesetz more commonly translated as Basic Law . The four individual laws that together make up the Constitution of Sweden . The Fundamental Laws of England . The Fundamental Law of Vatican City State The Basic Law s of a country which does not use the term constitution , or has an uncodified constitution. The fundamental physical law s of the universe Religion The Ten Commandments disambig es Leyes fundamentales fr Loi fondamentale ... more details
Fundamental science or basic science, pure science is science that describes the most basic object s, force s, relations between them and laws governing them, such that all other phenomena may be in principle derived from them following the logic of scientific reductionism . Physics is a typical fundamental science, chemistry is often included. There is a difference between fundamental science and applied science or practical science . ref American Association for the Advancement of Science, Science. 1917. Page 645 ref Fundamental science, in contrast to applied science, is defined as a fundamental knowledge it develops. The progress of fundamental science is based on well controlled experiments and careful observation. Fundamental science is dependent upon deductions from demonstrated truths, or is studied without regard to practical applications. Fundamental science has traditionally been associated with the natural sciences , however, research in the social science social and behavioral sciences can be deemed fundamental e.g., cognitive neuroscience, personality . See also Exact science Fundamental research Philosophy of science Scientific method Hard and soft science Hard science vs. Soft science References Reflist Further reading Henry James Clarke, http books.google.com books?id YBUHAAAAQAAJ The fundamental science . 1885. DEFAULTSORT Fundamental Science Category Philosophy of science science stub philosophy stub cy Gwyddoniaeth bur de Grundlagenwissenschaft et Alusteadused fr Science fondamentale it Scienza fondamentale nl Fundamentele wetenschap ja ru uk ... more details
A fundamental matrix may refer to fundamental matrix computer vision fundamental matrix linear differential equation disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
In representation theory of Lie group s and Lie algebra s, a fundamental representation is an irreducible finite dimensional representation of a semisimple Lie algebra semisimple Lie group or Lie algebra whose highest weight is a fundamental weight . For example, the defining module of a classical Lie group is a fundamental representation. Any finite dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to lie Cartan . Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite dimensional representations. Examples In the case of the general linear group , all fundamental representations are exterior power s of the defining module. In the case of the special unitary group SU n SU n , the n &minus 1 fundamental representations are the wedge products math operatorname Alt k mathbb C n math consisting of the alternating tensor s, for k 1, 2, ..., n &minus 1. The spin representation of the twofold cover of an odd orthogonal group , the odd spin group , and the two half spin representations of the twofold cover of an even orthogonal group, the even spinor group, are fundamental representations that cannot be realized in the space of tensors. The adjoint representation of the simple Lie group of type E8 mathematics E sub 8 sub is a fundamental representation. Explanation The Representation ... integral weights. It can be proved that there exists a set of fundamental weights , indexed by the vertices ... combinations of the fundamental weights. The corresponding irreducible representations are the fundamental representations of the Lie group. From the expansion of a dominant weight in terms of the fundamental weights one can take a corresponding tensor product of the fundamental representations ... uses Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer ... more details
about the type of unit of measure the concept in number theory Fundamental unit number theory A set of fundamental units is a set of Units of measurement units for physical quantity physical quantities from which every other unit can be generated. In the language of measurement , quantities are quantifiable aspects of the world, such as time , distance , velocity , mass , momentum , energy , and weight , and units are used to describe their measure. Many of these quantities are related to each other by various physical laws, and as a result the units of some of the quantities can be expressed as products ... that cannot be so expressed can be regarded as fundamental in this sense. There are other relationships between physical quantities which can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions ... of fundamental constants by one. For instance, time and distance are related to each other by the speed of light , c, which is a fundamental constant. It is possible to use this relationship to eliminate either the fundamental unit of time or that of distance. Similar considerations apply to Planck ... but not in others. In the SI system there are 7 fundamental units kilogram , meter , candela , second , ampere , kelvin , and mole unit mole . In theory a system of fundamental quantities or sometimes fundamental dimensions would be such that every other physical quantity or dimension of physical ... charge to such a number. One could similarly eliminate the mole as a fundamental unit by reference ... in terms of other physical quantities. That just leaves one fundamental dimension and one fundamental unit, but we still have plenty of fundamental constants left to eliminate that too for instance ... physicists who have cast doubt on the very existence of incompatible fundamental quantities. ref M. J. Duff, L. B. Okun and G. Veneziano, Trialogue on the number of fundamental constants , JHEP ... more details
Infobox Single Name Fundamental Love Cover ELT FundamentalLove.jpg Artist Every Little Thing band Every Little Thing from Album commonplace album commonplace Released July 30, 2003 Format CD single Recorded Genre J pop Length 10 16 Fundamental Love and nostalgia only Label AVEX Records avex trax Writer Kaori Mochida Producer Last single Grip br 2003 This single Fundamental Love br 2003 Next single Mata Ashita br 2003 nihongo Fundamental Love was the th single by the Japan ese j pop group Every Little Thing band Every Little Thing , released on July 30, 2003. Track listing nihongo Fundamental Love nostalgia 2003614 version nihongo Fundamental Love Instrumental Chart positions class wikitable align left Chart 2003 align center Peak br position align center Time in br chart align left Japan Oricon align center 9 align 7 weeks External links http avexnet.jp item every disc product AVCD 30501.html nihongo Fundamental Love information at AVEX Records Avex Network . http www.oricon.co.jp music release d 514178 1 nihongo Fundamental Love information at Oricon . Category 2003 singles Category Every Little Thing songs Category Songs written by Kaori Mochida Category Singles certified gold by the Recording Industry Association of Japan 2000s Japan single stub gl Fundamental Love ja ... more details
Unreferenced date December 2009 Dablink For the fundamental class in class field theory see class formation . In mathematics , the fundamental class is a homology mathematics homology class M associated to an oriented manifold M , which corresponds to the whole manifold , and pairing with which corresponds to integrating over the manifold . Intuitively, the fundamental class can be thought of as the sum of the top dimensional simplices of a suitable triangulation of the manifold. Definition Closed, orientable When M is a connected space connected orientable closed manifold of dimension n , the top homology group is infinite cyclic math H n M, mathbf Z cong mathbf Z math , and an orientation is a choice of generator, a choice of isomorphism math mathbf Z to H n M, mathbf Z math . The generator is called the fundamental class . If M is disconnected but still orientable , a fundamental class is a fundamental class for each connected component corresponding to an orientation for each component . It represents, in a sense, integration over M , and in relation with de Rham cohomology it is exactly that namely for M a smooth manifold, an differential form n form can be paired with the fundamental class as math langle omega, M rangle int M omega math to get a real number, which is the integral ..., one cannot define a fundamental class, or more precisely, one cannot define a fundamental class ... there is no ambiguity in choice of orientation , and has a math mathbf Z 2 math fundamental class. This math mathbf Z 2 math fundamental class is used in defining Stiefel Whitney numbers . With boundary ... of isomorphism is a fundamental class. Poincar duality Main Poincar duality Expand section date December 2008 Under Poincar duality , the fundamental class is dual to the bottom class of a connected ... decomposition of the flag variety of a Lie group , the fundamental class corresponds to the top dimension ... of a Coxeter group Poincar duality DEFAULTSORT Fundamental Class Category Algebraic topology ... more details
In geometry , the fundamental domain of a symmetry group of an object is a part or pattern, as small .... A fundamental domain is a subset of the space which contains exactly one point from each of these orbits .... There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected .... The images of a chosen fundamental domain under the group action then tessellation tile the space. One general construction of fundamental domains uses Voronoi cell s. Hints at general definition ... s, a fundamental domain also called fundamental region for this action is a set D of representatives ... quasi invariant measure mathematics measure on X . A fundamental domain always contains a free regular ..., but the repeated part has measure zero. This is a typical situation in ergodic theory . If a fundamental ... lattice Z sup n sup acting on it by translations, the quotient X G is the n dimensional torus . A fundamental ... fold rotation an orbit is either a set of n points around the axis, or a single point on the axis the fundamental ... on each side of the plane, or a single point in the plane the fundamental domain is a half space bounded ..., except for one orbit, consisting of the center only the fundamental domain is a half space bounded ... opposite to each other with respect to the axis, or a single point on the axis the fundamental ... the fundamental domain is an infinite slab for discrete translational symmetry in two directions the orbits are translates of a 2D lattice in the plane through the translation vectors the fundamental ... in three directions the orbits are translates of the lattice the fundamental domain is a primitive ... diagram. In the case of translational symmetry combined with other symmetries, the fundamental domain is part of the primitive cell. For example, for wallpaper group s the fundamental domain is a factor 1, 2, 3, 4, 6, 8, or 12 smaller than the primitive cell. Fundamental domain for the modular group ... set of H &Gamma the grey one with the third point of the triangle at infinity is the canonical fundamental ... more details
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