In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with...

Haken conjecture for closed hyperbolic 3-manifolds. The proof built on results of Kahn and Markovic in their proof of the Surface subgroup conjecture and...

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

an essential ingredient the freshly-obtained solution to the surface subgroup conjecture by Jeremy Kahn and Vladimir Markovic. Other results which are...

In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure...

2009) Surface subgroup conjecture (Jeremy Kahn, Vladimir Markovic, 2009) Normal scalar curvature conjecture and the Böttcher–Wenzel conjecture (Zhiqin...

a ceremony at Oxford University. Surface subgroup conjecture Virtually Haken conjecture Virtually fibered conjecture "2012 Clay Research Conference"....

subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of...

hyperbolic 3-manifold (proof of the surface subgroup conjecture) and for their proof of the Ehrenpreis conjecture. In 2014 he was an invited speaker at...

by subgroups of SL2(R), particularly, the normalizer Γ0(p)+ of the Hecke congruence subgroup Γ0(p) in SL(2,R). They found that the Riemann surface resulting...

Calabi (1954, 1957) who first conjectured that such surfaces might exist, and Shing-Tung Yau (1978) who proved the Calabi conjecture. Calabi–Yau manifolds are...

of the conjectures were logically related to the virtually Haken conjecture. In order of strength they are: (the surface subgroup conjecture) The fundamental...

closed hyperbolic 3-manifolds. Virtually Haken conjecture Surface subgroup conjecture Ehrenpreis conjecture Thurston 1982, p. 380. Bergeron, Nicolas; Wise...

Euclidean 3-space. Carathéodory conjecture: This conjecture states that a closed convex three times differentiable surface admits at least two umbilic points...

K3 surface over a field is projective.) By Shing-Tung Yau's solution to the Calabi conjecture, it follows that every complex analytic K3 surface has...

a conjecture of Gauss on the mean order of class groups of real quadratic fields. Arithmetic surfaces can be used to construct families of surfaces of...

{\displaystyle \Gamma } defining the Bolza surface is also a subgroup of the (3,3,4) triangle group, which is a subgroup of index 2 in the ( 2 , 3 , 8 ) {\displaystyle...

Brieskorn–Grothendieck resolution General elephant conjecture du Val, Patrick (1934a). "On isolated singularities of surfaces which do not affect the conditions of...

275: 786–789. McCarthy, John (1985). "A "Tits-alternative" for subgroups of surface mapping class groups". Trans. Amer. Math. Soc. 291: 583–612. doi:10...

subgroup of a topological group G is a subgroup H whose relative topology is the discrete one. For example, the integers, Z, form a discrete subgroup...

group Borel subgroup Radical of an algebraic group Unipotent radical Lie-Kolchin theorem Haboush's theorem (also known as the Mumford conjecture) Group scheme...

fake projective surfaces are called fake projective spaces. As a consequence of the work of Aubin and Yau on solution of Calabi Conjecture in the case of...

finite-index subgroups and the congruence subgroup problem roughly asks whether all subgroups are obtained in this way. The conjecture (usually attributed...

in topology. The solution by Stephen Smale, in 1961, of the Poincaré conjecture in five or more dimensions made dimensions three and four seem the hardest;...

^{3}/\Gamma } where Γ {\displaystyle \Gamma } is a discrete subgroup of PSL(2,C). Here, the subgroup Γ {\displaystyle \Gamma } , a Kleinian group, is defined...

proved William Thurston's key conjecture that every closed hyperbolic 3-manifold contains an almost geodesic immersed surface. Marković was also awarded...

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers...

conjecture may refer to one of several conjectural statements from differential geometry and topology attributed to Heinz Hopf. The Hopf conjecture is...

Loop theorem K-theory of a category Smith conjecture Surface subgroup conjecture Virtually Haken conjecture History of knot theory Waldhausen category...

zeta function Selberg zeta function of a Riemann surface Shimizu L-function Shintani zeta function Subgroup zeta function Witten zeta function of a Lie group...