numbers under the Collatz map. The Collatzconjecture is equivalent to the statement that all ... graph showing the orbits of the first 1000 numbers. The Collatzconjecture is an unsolved conjecture in mathematics named after Lothar Collatz , who first proposed it in 1937. The conjecture is also ... the Collatzconjecture Mathematics is not yet ready for such problems. He offered 500 for its solution ... 4 5a i 1 2 1 a i 1 1 math The Collatzconjecture is This process will eventually reach the number 1 ... of the conjecture In reverse Image Collatz graph 20 iterations.svg thumb 200px The first 20 ..., add the numerator and denominator 255 256 511 . The Collatzconjecture then says that the numerator ... Conjecture can be rephrased as stating that the Collatz parity sequence for every number eventually ... De Mol. The Collatzconjecture equivalently states that this tag system, with an arbitrary finite ... 55 164 82 41 122 61 182 91 272 136 68 34 17 7 18 The Generalized CollatzConjecture is the assertion ... for a counterexample to the Collatzconjecture, this precomputation leads to an even more important ... to the Collatzconjecture, there is a k for which such an inequality holds, so checking the Collatz ... How to Construct a Counterexample to the CollatzConjecture De Mol, Liesbeth, Tag systems and Collatz ... of the Collatz problem and conjecture , 29 October 2008, Number Theory category in arXiv preprint ... content qx6pxm4jufn24a5t About the Collatzconjecture , Acta Informatica , Berlin Heidelberg ... Paul, http www.logika.umk.pl llp 141 jpvb.pdf The CollatzConjecture A Case Study in Mathematical Problem ... 337 , E17 Permutation Sequences and the CollatzConjecture. General Distributed Computing http boinc.thesonntags.com collatz project that verifies the Collatzconjecture for larger values. An ongoing ... tos 3x 1.html project by Tom s Oliveira e Silva continues to verify the Collatzconjecture with fewer ... number up to 500 digits in length. DEFAULTSORT CollatzConjecture Category Articles with inconsistent ... more details
Collatz can refer to Lothar Collatz , German mathematician, who proposed several ideas Collatzconjecture , number theory conjecture on Collatz sequences disambig ... more details
File Lothar Collatz.jpg thumb Photo courtesy MFO Lothar Collatz July 6, 1910, Arnsberg , Westphalia September 26, 1990, Varna , Bulgaria was a Germany German mathematician . In 1937 he posed the famous Collatzconjecture , which remains unsolved. The Collatz Wielandt formula for positive matrices important in Perron Frobenius theorem is named after him. Collatz studied at different universities in Germany ... . For his many contributions to the field, Collatz had many honors bestowed upon him in his lifetime ... died in Varna , Bulgaria, while attending a mathematics conference. References Lothar Collatz July ... by G nter Meinardus and G nther N rnberger citation first Lothar last Collatz author link Lothar Collatz ..., P Hagedorn and W Velte, Lothar Collatz German , Numerical treatment of eigenvalue problems, Vol. 5, Oberwolfach, 1990 Birkh user, Basel, 1991 , viii ix. R Ansorge, Lothar Collatz 6 July 1910 26 September ... Collatz auf die angewandte Mathematik, Numerical mathematics, Sympos., Inst. Appl. Math., Univ. Hamburg ... Collatz on the occasion of his 75th birthday, Linear Algebra Appl. 68 1985 , vi 1 8. R B Guenther, Obituary Lothar Collatz, 1910 1990, Aequationes Math. 43 2 3 1992 , 117 119. H Heinrich, Zum siebzigsten Geburtstag von Lothar Collatz, Z. Angew. Math. Mech. 60 5 1980 , 274 275. G Meinardus, G N rnberger, Th Riessinger and G Walz, In memoriam the work of Lothar Collatz in approximation theory, J. Approx. Theory 67 2 1991 , 119 128. G Meinardus and G N rnberger, In memoriam Lothar Collatz July 6, 1910 September 26, 1990 , J. Approx. Theory 65 1 1991 , i 1 2. J R Whiteman, In memoriam Lothar Collatz ... Collatz MathGenealogy id 20676 Persondata Metadata see Wikipedia Persondata . NAME Collatz, Lothar ... Collatz, Lothar Category 1910 births Category 1990 deaths Category 20th century mathematicians ... Germany mathematician stub da Lothar Collatz de Lothar Collatz fr Lothar Collatz ht Lothar Collatz ja pl Lothar Collatz pt Lothar Collatz sk Lothar Collatz ... more details
The abc conjecture P versus NP problem P NP The Collatzconjecture Beal s conjecture The Poincar theorem proven by Grigori Perelman The Goldbach s conjecture The Langlands program is a far reaching web of these ideas of unifying conjecture s that link different subfields of mathematics, e.g. number ... search farther than previously done. For instance, the Collatzconjecture , which concerns whether ...No footnotes date August 2010 A conjecture is a Proposition philosophy proposition that is Formal proof unproven but is believed to be true and has not been disproven. Karl Popper pioneered the use of the term conjecture in scientific philosophy . Conjecture is contrasted by hypothesis hence theory , axiom , principle , which is a testable statement based on accepted grounds. In mathematics , a conjecture is an unproven proposition or theorem that appears correct. Famous conjectures One famous conjecture was Fermat s Last Theorem . Citation needed date July 2010 The conjecture taunted mathematicians ... supporting a conjecture, no matter how large, is insufficient for establishing the conjecture s veracity, since a single counterexample would immediately bring down the conjecture. Conjectures disproven through counterexample are sometimes referred to as false conjectures cf. P lya conjecture ... mathematics. Use of conjectures in conditional proofs Sometimes a conjecture is called a hypothesis ..., the Riemann hypothesis is a conjecture from number theory that amongst other things makes predictions ... of this conjecture. These are called conditional proof s the conjectures assumed appear ... or falsity of conjectures of this type. Undecidable conjectures Not every conjecture ends up being proven ... of conjectures External links Wiktionary conjecture http garden.irmacs.sfu.ca Open Problem Garden ... eo Konjekto matematiko fr Conjecture gd Baralachas hi id Konjektur it Congettura ... ru simple Conjecture sk Domnienka fi Konjektuuri sv F rmodan th tr Konjekt r ... more details
The mathematician Leonard Euler 1707 1783 made several different conjectures which are all called Euler s conjecture Euler s sum of powers conjecture Euler s conjecture Waring s problem disambig Category Mathematical disambiguation th ... more details
In mathematics , there are a number of so called Deligne conjectures , provided by Pierre Deligne . These are independent conjecture s in various fields of mathematics. The Deligne conjecture in deformation theory is about the operad operadic structure on Hochschild cohomology . It was proved by Kontsevich Soibelman, McClure Smith and others. It is of importance in relation with string theory . The Deligne conjecture on special values of L functions is a formulation of the hope for Algebraic number algebraicity of L n where L is an L function and n is an integer in some set depending on L . There is a Deligne conjecture on 1 motives arising in the theory of motive algebraic geometry motives in algebraic geometry . There is a Gross Deligne conjecture in the theory of complex multiplication . There is a Deligne conjecture on monodromy , also known as the weight monodromy conjecture , or purity conjecture for the monodromy filtration . There is E7 Lie algebra Deligne conjecture in the representation theory of the exceptional Lie group s. There is a Deligne Langlands conjecture of historical importance in relation with the development of the Langlands philosophy . disambig Category Algebraic geometry Category Conjectures ... more details
In mathematics , Jean Pierre Serre has suggested a number of conjectural or formerly conjectural results The Serre conjecture number theory Serre conjecture concerning Galois representations The Quillen Suslin theorem , formerly known as Serre s conjecture Serre s multiplicity conjectures in commutative algebra Serre s conjecture II algebra Serre s Conjecture II concerning the Galois cohomology of linear algebraic group s. mathdab Category Conjectures ... more details
There are several conjectures in mathematics by David Mumford . Mumford s conjecture about reductive groups, now called Haboush s theorem . The Mumford conjecture on the cohomology of the stable mapping class group , proved by Ib Madsen and Michael Weiss. The Manin Mumford conjecture about Jacobians of curves, proved by Michel Raynaud. mathdab ... more details
In mathematics, there are several conjectures made by Emil Artin Artin conjecture L functions Artin s conjecture on primitive roots The now proved conjecture that finite fields are quasi algebraically closed see Chevalley Warning theorem . The now disproved conjecture that any algebraic form over the p adics of degree d in more than d sup 2 sup variables represents zero. For this see Ax Kochen theorem or Brauer s theorem . Artin had also conjectured Hasse s theorem on elliptic curves disambig DEFAULTSORT Artin Conjecture Category Analytic number theory Category Algebraic number theory Category Conjectures fr Conjecture d Artin ... more details
The prolific mathematician Paul Erd s and his various collaborators made many famous mathematical conjecture s, over a wide field of subjects. Some of these are the following The Cameron Erd s conjecture on sum free sets of integers, proved by Ben J. Green Ben Green . The Erd s Burr conjecture on Ramsey numbers of graphs. The Erd s Faber Lov sz conjecture on coloring unions of cliques. The Erd s Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity. The Erd s Gy rf s conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3. The Erd s Hajnal conjecture that in a family of graphs defined by an excluded induced ..., Discrete Applied Mathematics 25 1989 37 52 The Restricted sumset Erd s Heilbronn conjecture in combinatorial ... Dias da Silva and Y.O. Hamidoune in 1994. The Erd s Lov sz conjecture on weak strong delta systems ... Erd s Mollin Walsh conjecture on consecutive triples of powerful numbers. The Erd s Menger conjecture ... Aharoni and Eli Berger The Erd s Selfridge conjecture that a covering set contains at least one odd member. The Erd s Stewart conjecture on the Diophantine equation n 1 p sub k sub sup a sup p sub k 1 sub sup b sup solved by Luca, MR 2001g 11042 The Erd s Straus conjecture on the Diophantine equation 4 n 1 x 1 y 1 z . The Erd s conjecture on arithmetic progressions in sequences with divergent sums of reciprocals. The Erd s Woods number Erd s Woods conjecture on numbers determined by the set of prime divisors of the following k numbers. The Erd s Szekeres conjecture ... Tur n conjecture on additive bases of natural numbers. A conjecture on Sylvester s sequence quickly growing integer sequences with rational reciprocal series . A conjecture on equitable coloring s proven ..., Open problems of Paul Erd s in graph theory disambig Category Conjectures Erdos conjecture Category Mathematical disambiguation Erdos conjecture Category Paul Erd s Conjecture it Congettura di Erd s ... more details
There are two main conjectures known as the Hadwiger conjecture or Hadwiger s conjecture Hadwiger conjecture graph theory , a relationship between the number of colors needed by a given graph and the size of its largest clique minor Hadwiger conjecture combinatorial geometry that for any n dimensional convex body, at most 2 sup n sup smaller homothetic bodies are necessary to contain the original See also Hadwiger Nelson problem on the chromatic number of unit distance graphs in the Euclidean plane Hadwiger s theorem characterizing measure functions in Euclidean spaces disambig ... more details
No footnotes date January 2010 Legendre s conjecture , proposed by Adrien Marie Legendre , states that there is a prime number between n sup 2 sup and n 1 sup 2 sup for every positive integer n . The conjecture is one of Landau s problems 1912 and unproven as of 2010 lc on . The prime number theorem suggests the actual number of primes between n sup 2 sup and n 1 sup 2 sup OEIS A014085 is about n log n , i.e. about as many as the Prime counting function number of primes less than or equal to n . If Legendre s conjecture is true, the prime gap gap between any two successive primes would be math O sqrt p math . In fact the conjecture follows from Andrica s conjecture . Harald Cram r Cram r s conjecture conjectured that the gap is always much smaller, math O log 2 p math if Cram r s conjecture is true, Legendre s conjecture would follow. Cram r also proved that the Riemann hypothesis implies a weaker bound of math O sqrt p log p math on the size of the largest prime gaps. Legendre s conjecture implies that at least one prime can be found in every revolution of the Ulam spiral . Legendre s conjecture follows from Opperman s conjecture . See also Brocard s conjecture Oppermann s conjecture External links mathworld urlname LegendresConjecture title Legendre s conjecture Category Conjectures about prime numbers Category Unsolved problems in mathematics Numtheory stub ca Conjectura de Legendre de Legendresche Vermutung es Conjetura de Legendre fr Conjecture de Legendre it Congettura di Legendre nl Vermoeden van Legendre pt Conjectura de Legendre zh ... more details
The term Weil conjecture may refer to The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne and others. The Modularity theorem Taniyama Shimura Weil conjecture about elliptic curves, proved by Wiles and others. The Weil conjecture on Tamagawa numbers about the Tamagawa number of an algebraic group , proved by Kottwitz and others. mathdab ... more details
In number theory , Lemoine s conjecture , named after mile Lemoine , also known as Levy s conjecture , after Hyman Levy , states that all odd integer s greater than 5 can be represented as the sum of an odd prime number and an even semiprime . To put it algebraically, 2 n 1 p 2 q always has a solution in primes p and q not necessarily distinct for n 2. The Lemoine conjecture is similar to but stronger than Goldbach s weak conjecture . For example, 47 13 2 17 37 2 5 41 2 3 43 2 2. OEIS id A046927 counts how many different ways 2 n 1 can be represented as p 2 q . According to MathWorld , the conjecture has been verified by Corbitt up to 10 sup 9 sup . The conjecture was posed by mile Lemoine in 1895, but in more recent years came to be attributed to Hyman Levy who pondered it in the 1960s. See also mile Lemoine Lemoine s conjecture and extensions Lemoine s conjecture and extensions References Emile Lemoine, L interm diare des math maticiens , 1 1894 , 179 ibid 3 1896 , 151. H. Levy, On Goldbach s Conjecture , Math. Gaz. 47 1963 274 L. Hodges, A lesser known Goldbach conjecture , Math. Mag. , 66 1993 45 47. John O. Kiltinen and Peter B. Young, Goldbach, Lemoine, and a Know Don t Know Problem , Mathematics Magazine , Vol. 58, No. 4 Sep., 1985 , pp. 195 203 http www.jstor.org stable 2689513?seq 7 Richard K. Guy , Unsolved Problems in Number Theory New York Springer Verlag 2004 C1 External links MathWorld title Levy s Conjecture urlname LevysConjecture http demonstrations.wolfram.com LevysConjecture Levy s Conjecture by Jay Warendorff, Wolfram Demonstrations Project . Category Additive number theory Category Conjectures about prime numbers it Congettura di Levy zh ... more details
nofootnotes date February 2010 Orphan date December 2009 In mathematics , the Nakai conjecture states that if V is a complex algebraic variety , such that its ring of differential operators is generated by the derivation algebra derivations it contains, then V is a smooth variety . This is the conjectural converse to a result of Alexander Grothendieck . It is known to be true for algebraic curve s. The conjecture was proposed by the Japanese mathematician Yoshikazu Nakai. A consequence would be the Zariski Lipman conjecture , for a complex affine variety V with coordinate ring R if the derivations of R are a free module over R , then V is smooth. Sources Google Scholar results for http scholar.google.com scholar?q nakai 20conjecture&oe utf 8&rls com.ubuntu en US official&client firefox a&um 1&ie UTF 8&sa N&hl en&tab ws nakai conjecture DEFAULTSORT Nakai Conjecture Category Algebraic geometry Category Singularity theory Category Conjectures ... more details
This page concerns mathematician Sergei Novikov s topology conjecture. For astrophysicist Igor Novikov s conjecture regarding time travel, see Novikov self consistency principle . The Novikov conjecture is one of the most important unsolved problems in topology . It is named for Sergei Novikov mathematician Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomial s in the Pontryagin class es of a manifold mathematics manifold , arising from the fundamental group . According to the Novikov conjecture, the higher signatures , which are certain numerical invariants of smooth manifolds, are homotopy invariants. The conjecture has been proved for finitely generated abelian groups . It is not yet known whether the Novikov conjecture holds true for all groups. There are no known counterexamples to the conjecture. Precise formulation of the conjecture Let G be a discrete group and BG its classifying space , which is a Eilenberg Maclane space K G,1 and therefore unique up to homotopy equivalence as a CW complex. Let math f M rightarrow BG math be a continuous map from a closed oriented n dimensional manifold M to BG , and math x in H n 4i BG mathbb Q . math Novikov considered the numerical expression, found by evaluating ... bundle. The Novikov conjecture states that the higher signature is a homotopy invariant for every such map f and every such class x . Connection with the Borel conjecture The Novikov conjecture is equivalent to the rational injectivity of the assembly map in L theory . The Borel conjecture ... Novikov http www.math.umd.edu jmr NC.html Novikov Conjecture Bibliography http www.maths.ed.ac.uk aar books novikov1.pdf Novikov Conjecture 1993 Oberwolfach Conference Proceedings, Volume 1 http www.maths.ed.ac.uk aar books novikov2.pdf Novikov Conjecture 1993 Oberwolfach Conference Proceedings, Volume ... notes on the Novikov Conjecture pdf http www.scholarpedia.org article Novikov conjecture Scholarpedia ... more details
In mathematics , specifically geometric topology , the Borel conjecture asserts that an Aspherical space aspherical closed manifold is determined by its fundamental group , up to homeomorphism . It is a Rigidity mathematics rigidity conjecture, demanding that a weak, algebraic notion of equivalence namely, a homotopy homotopy equivalence imply a stronger, topological notion namely, a homeomorphism . Precise formulation of the conjecture Let math M math and math N math be closed manifold closed and Aspherical space aspherical topological manifold s, and let math f M to N math be a homotopy homotopy equivalence . The Borel conjecture states that the map math f math is homotopic to a homeomorphism ... conjecture implies that aspherical closed manifolds are determined, up to homeomorphism, by their fundamental groups. This conjecture is false if topological manifold s and homeomorphisms are replaced ... sum with an exotic sphere . The origin of the conjecture In a May 1953 letter to Jean Pierre Serre ... fundamental groups are homeomorphic. Motivation for the conjecture A basic question is the following ... manifold s is homotopic to an isometry in particular, to a homeomorphism. The Borel conjecture .... Relationship to other conjectures The Borel conjecture implies the Novikov conjecture for the special ... conjecture asserts that a closed manifold homotopy equivalent to math S 3 math , the 3 sphere , is homeomorphic to math S 3 math . This is not a special case of the Borel conjecture, because math S 3 math is not aspherical. Nevertheless, the Borel conjecture for the Torus 3 torus math T 3 S 1 times S 1 times S 1 math implies the Poincar conjecture for math S 3 math . References F.T. Farrell, The Borel conjecture. Topology of high dimensional manifolds, No. 1, 2 Trieste, 2001 , 225 298, ICTP Lect ... conjecture. Geometry and algebra. Oberwolfach Seminars, 33. Birkh user Verlag, Basel, 2005. http www.maths.ed.ac.uk aar surgery borel.pdf The birth of the Borel conjecture , Extract from letter from ... more details
In mathematics , the Seifert conjecture states that every nonsingular, continuous vector field on the 3 sphere has a closed orbit. It is named after Herbert Seifert . In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non existence as a conjecture. He also established the conjecture for perturbations of the Hopf fibration . The conjecture was disproven in 1974 by Paul Schweitzer , who exhibited a math C 1 math counterexample. Schweitzer s construction was then modified by Jenny Harrison in 1988 to make a math C 2 delta math counterexample for some math delta 0 math . The existence of smoother counterexamples remained an open question until 1993 when Krystyna Kuperberg constructed a very different math C infty math counterexample. Later this construction was shown to have real analytic and piecewise linear versions. References V. Ginzburg and B. G rel, http front.math.ucdavis.edu math.DG 0110047 A math C 2 math smooth counterexample to the Hamiltonian Seifert conjecture in math R 4 math , Ann. of Math. 2 158 2003 , no. 3, 953 976 J. Harrison, math C 2 math counterexamples to the Seifert conjecture , Topology 27 1988 , no. 3, 249 278. G. Kuperberg A volume preserving counterexample to the Seifert conjecture , Comment. Math. Helv. 71 1996 , no. 1, 70 97. K. Kuperberg A smooth counterexample to the Seifert conjecture , Ann. of Math. 2 140 1994 , no. 3, 723 732. G. Kuperberg and K. Kuperberg, http front.math.ucdavis.edu math.DS 9802040 Generalized counterexamples to the Seifert conjecture , Ann. of Math. 2 143 1996 , no. 3, 547 576. H. Seifert, Closed integral curves in 3 space and isotopic two dimensional deformations , Proc. Amer. Math. Soc. 1, 1950 . 287 302. P. A. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliations , Ann. of Math. 2 100 1974 , 386 400. Further reading K. Kuperberg, http www.ams.org notices 199909 fea kuperberg.pdf Aperiodic dynamical systems . Notices Amer. Math. Soc. 46 1999 , no. 9 ... more details
Beal s conjecture is a conjecture in number theory proposed by Andrew Beal in about 1993 a similar conjecture was suggested independently at about the same time by Andrew Granville . While investigating generalizations of Fermat s last theorem in 1993, Beal formulated the following conjecture If math A x B y C z, , math where A , B , C , x , y , and z are positive integers with x , y , z 2 then A , B , and C must have a common prime divisor factor . Beal has offered a prize of USD US 100,000 for a proof of his conjecture or a counterexample ref http www.math.unt.edu mauldin beal.html The Beal Conjecture Bot generated title ref . Examples To illustrate, the solution 3 sup 3 sup 6 sup 3 sup 3 sup 5 sup has bases with a common factor of 3, and the solution 7 sup 6 sup 7 sup 7 sup 98 sup 3 sup has bases with a common factor of 7. Indeed the equation has infinitely many solutions, including for example math left a left a m b m right right m left b left a m b m right right m left a m b m right ... is a counterexample to the conjecture, since the bases all have the factor math a m b m math in common. The example 7 sup 3 sup 13 sup 2 sup 2 sup 9 sup shows that the conjecture is false if one of the exponents ... , this conjecture has been verified for all values of all six Variable mathematics variables up to 1000. ref http www.norvig.com beal.html Beal s Conjecture A Search for Counterexamples Bot generated .... A variation of the conjecture where x , y , z instead of A , B , C must have a common prime factor is not true. See, for example math 27 4 162 3 9 7 math . Beal s conjecture is a generalization of Fermat ... factor, it can be divided out of each to yield an equation with smaller, coprime bases. The conjecture .... Daniel Mauldin title A Generalization of Fermat s Last Theorem The Beal Conjecture and Prize Problem ... 199711 beal.pdf PlanetMath title Beal s Conjecture urlname BealsConjecture http mathoverflow.net questions 28764 status of beal tijdeman zagier conjecture DEFAULTSORT Beal s Conjecture Category Number ... more details
In algebra the Dixmier conjecture , asked by harvtxt Dixmier 1968 loc problem 1 , is the conjecture that any endomorphism of a Weyl algebra is an automorphism. harvtxt Belov Kanel Kontsevich 2007 showed that the Dixmier conjecture generalized to Weyl algebras with more generators is equivalent to the Jacobian conjecture . References Citation last1 Dixmier first1 Jacques title Sur les alg bres de Weyl url http www.numdam.org item?id BSMF 1968 96 209 0 mr 0242897 year 1968 journal Bulletin de la Soci t Math matique de France volume 96 pages 209 242 Tsuchimoto, Yoshifumi. Endomorphisms of Weyl algebra and p curvatures . Osaka J. Math. 42 2005 , 435 452. Citation last1 Belov Kanel first1 Alexei last2 Kontsevich first2 Maxim title The Jacobian conjecture is stably equivalent to the Dixmier conjecture arxiv math 0512171 mr 2337879 year 2007 journal Moscow Mathematical Journal volume 7 issue 2 pages 209 218 Category Algebra Category Conjectures algebra stub ... more details
In the mathematical subject of knot theory , the Berge conjecture states that the only knot mathematics knot s in the 3 sphere which admit lens space Dehn surgery surgeries are Berge knot s. The conjecture and family of Berge knots is named after John Berge . Progress on the conjecture has been slow. Recently Yi Ni proved that if a knot admits a lens space surgery, then it is fibered knot fibered . Berge knots are fibered. External links Two blog posts in the weblog Low Dimensional Topology Recent Progress and Open Problems related to the Berge conjecture http ldtopology.wordpress.com 2007 11 19 the berge conjecture The Berge conjecture , by Jesse Johnson http ldtopology.wordpress.com 2008 06 30 knot complements covering knot complements Knot complements covering knot complements by Ken Baker References Yi Ni. Knot Floer homology detects fibred knots. Invent. Math. 170 2007 , no. 3, 577 608. Yi Ni. Corrigendum to http arxiv.org pdf 0808.0940v1 Knot Floer homology detects fibred knots pdf original ref link http arxiv.org abs 0808.0940 arXiv 0808.0940v1 Category Knot theory Category 3 manifolds topology stub ... more details
In mathematics , Blattner s conjecture was a description of the discrete series representation s of a general semisimple group G in terms of their restricted representation s to a maximal compact subgroup K their so called K types , formulated by Robert J Blattner . At the time, direct constructions of the discrete series were not known. The conjecture was proved by Hecht and Schmid in 1975. The result is now often known as the Blattner formula . References H. Hecht and W. Schmid, A proof of Blattner s conjecture , Invent. Math., 31 1975 , 129 154 Category Representation theory of Lie groups Category Conjectures Category Mathematical theorems ... more details
The mathematician Irving Kaplansky is notable for proposing numerous conjecture s in several branches of mathematics , including a list of ten conjectures on Hopf algebra s. They are usually known as Kaplansky s conjectures . NOTOC Kaplansky s conjecture on group rings Kaplansky s conjecture on group rings states that the complex group ring C G of a torsion free group G has no nontrivial idempotent s. It is related to the Richard Kadison Kadison idempotent conjecture, also known as the Kadison&ndash Kaplansky conjecture. Kaplansky s conjecture on Banach algebras This conjecture states that every algebra homomorphism from the Banach algebra C X where X is a compact space compact Hausdorff space Hausdorff topological space into any other Banach algebra, is necessarily continuous function continuous . The conjecture is equivalent to the statement that every algebra norm on C X is equivalent to the usual uniform norm . Kaplansky himself had earlier shown that every complete algebra norm on C X is equivalent to the uniform norm. In the mid 1970s, H. Garth Dales and J. Esterle independently proved that, if one furthermore assumes the validity of the continuum hypothesis , there exist compact Hausdorff spaces X and discontinuous homomorphisms from C X to some Banach algebra, giving counterexamples to the conjecture. In 1976, Robert M. Solovay R. M. Solovay proved building on work of H. Woodin that there is at least one model of ZFC Zermelo&ndash Fraenkel set theory axiom of choice in which Kaplansky s conjecture is true. Necessarily, in such a model the continuum hypothesis is false. Combined with the results of Dales and Esterle, this shows that the conjecture is independence mathematical logic independent of the axiom s of ZFC. See also List of statements undecidable in ZFC References H. G. Dales, Automatic continuity a survey . Bull. London Math. Soc. 10 1978 , no. 2, 129 ... conjecture for word hyperbolic groups . Invent. Math. 149 2002 , no. 1, 153 194. algebra stub ... more details
other uses Honeycomb disambiguation Image Hexagons.jpg thumb right A regular hexagonal grid The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter. The conjecture was proposed by Pappus of Alexandria c. 290 c. 350 and proved by mathematician Thomas C. Hales . ref Cite web last Weisstein first Eric W. publisher MathWorld title Honeycomb Conjecture url http mathworld.wolfram.com HoneycombConjecture.html accessdate 27 Dec 2010 ref ref Cite journal last Hales first Thomas C. title The Honeycomb Conjecture date 8 Jun 1999 arxiv math 9906042 journal Discrete and Computational Geometry volume 25 pages 1 22 2001 ref References reflist Category Discrete geometry Category Euclidean plane geometry geometry stub fr Th or me du nid d abeille ... more details
The Whitehead conjecture is a claim in algebraic topology . It was formulated by J. H. C. Whitehead in 1941. It states that every Connectedness connected subcomplex of a two dimensional Aspherical space aspherical CW complex is aspherical. In 1997, Mladen Bestvina and Noel Brady constructed a group G so that either G is a counterexample to the Eilenberg Ganea conjecture , or there must be a counterexample to the Whitehead conjecture. References http links.jstor.org sici?sici 0003 486X 28194104 292 3A42 3A2 3C409 3AOARTHG 3E2.0.CO 3B2 5 J. H. C. Whitehead, On adding relations to homotopy groups , Annals of Mathematics, 2nd Ser., 42 1941 , no. 2, 409 &ndash 428. http www.springerlink.com content nhj24dgb0vb7bx5p ?p 3b9c54d35a7c445587b1fc97576a6a83&pi 1 Mladen Bestvina, Noel Brady, Morse theory and finiteness properties of groups , Inventiones Mathematicae 129 1997 , no. 3, 445 &ndash 470. DEFAULTSORT Whitehead Conjecture Category Algebraic topology Category Conjectures ... more details
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