In geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group...

theorem Borel right process Borel set Borel summation Borel distribution Borel's conjecture about strong measure zero sets (not to be confused with Borel conjecture...

uncountable set of Lebesgue measure 0 which is not of strong measure zero. Borel's conjecture states that every strong measure zero set is countable. It is now...

 452) Borel–Weil–Bott theorem Borel cohomology Borel conjecture Borel construction Borel subgroup Borel subalgebra Borel fixed-point theorem Borel's theorem...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

{\displaystyle f} . The Novikov conjecture is equivalent to the rational injectivity of the assembly map in L-theory. The Borel conjecture on the rigidity of aspherical...

Bing–Borsuk conjecture: every n {\displaystyle n} -dimensional homogeneous absolute neighborhood retract is a topological manifold. Borel conjecture: aspherical...

(1979). "A counterexample to the "generalized Ramanujan conjecture" for (quasi-) split groups". In Borel, Armand; Casselman, Bill (eds.). Automorphic forms...

Margulis. Qualitative versions of the Oppenheim conjecture were later proved by Eskin–Margulis–Mozes. Borel and Prasad established some S-arithmetic analogues...

In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular...

to resolving several other unsolved conjectures. These include a conjecture of Paul Erdős on the existence of Borel subrings of the real numbers with fractional...

Farrell-Jones Conjecture for hyperbolic groups", arXiv:math/0609685 Bartels, Arthur; Lück, Wolfgang; Reich, Holger (2009), The Borel Conjecture for hyperbolic...

general conjecture of Margulis on Lie groups. Borel showed in 1909 that the exceptional set of real pairs (α,β) violating the statement of the conjecture is...

H^{3}} are called Fuchsian groups and Kleinian groups, respectively. Borel conjecture Goldberg, Samuel I. (1998), Curvature and Homology, Dover Publications...

Borel–Cantelli lemma. The converse implication is the crux of the conjecture. There have been many partial results of the Duffin–Schaeffer conjecture...

expositions of their work. Borel (1979) and Vogan (1993) discuss the Langlands conjectures for more general groups. The Langlands conjectures for arbitrary reductive...

Bordigism Armand Borel, French mathematician – Borel–Weil–Bott theorem, Borel conjecture, Borel fixed-point theorem, Borel's theorem Émile Borel, French mathematician...

Weil conjecture, around 1967, which later under pressure from Serge Lang (resp. of Jean-Pierre Serre) became known as the Taniyama–Shimura conjecture (resp...

Thomas Farrell he worked on a program to prove the Novikov conjecture and the Borel conjecture with methods from geometric topology and gave proofs for...

intervals (In) which covers X and such that In has length at most εn. Borel's conjecture, that every strong measure zero set is countable, is independent of...

to show that Borel's conjecture, which says that all strong measure zero sets are countable, is consistent with ZFC. (Borel's conjecture is not consistent...

conjecture on homotopy invariance of higher signatures, the Baum–Connes conjecture on K-theory of group C*-algebras, and the stable Borel conjecture on...

Examples are the classification of exotic spheres, and the proofs of the Borel conjecture for negatively curved manifolds and manifolds with hyperbolic fundamental...

as Blotto game). Borel conjectured the non-existence of mixed-strategy equilibria in finite two-person zero-sum games, a conjecture that was proved false...

In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them...

See Betti number. Bing–Borsuk conjecture See Bing–Borsuk conjecture. Bockstein homomorphism Borel Borel conjecture. Borel–Moore homology Borsuk's theorem...

and dynamics to questions such as the Borel conjecture. The Farrell-Jones conjecture implies the Borel Conjecture for manifolds of dimension greater than...

i {\displaystyle K=\bigcup _{i=1}^{\infty }K_{i}} , where each Ki is a Borel set, then γ ( K ) ≤ C ∑ i = 1 ∞ γ ( K i ) {\displaystyle \gamma (K)\leq...

of analytic determinacy (from the existence of a measurable cardinal), Borel determinacy (from ZFC alone), the proof (with John R. Steel) of projective...

theory Borel-Serre Compactification Grothendieck-Serre Correspondence Serre class Quillen–Suslin theorem (sometimes known as "Serre's Conjecture" or "Serre's...