In geometry, Thurston's geometrization theorem or hyperbolization theorem implies that closed atoroidal Haken manifolds are hyperbolic, and in particular...

conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture...

conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture...

his celebrated hyperbolic Dehn surgery theorem. To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important...

in Thurston's proof of the hyperbolization theorem for the case of manifolds that fiber over the circle. By Bers's theorem, quasi-Fuchsian groups (of...

In geometry, geometrization theorem may refer to Thurston's hyperbolization theorem for Haken 3-manifolds Thurston's geometrization conjecture proved...

manifolds. The hierarchy played a crucial role in William Thurston's hyperbolization theorem for Haken manifolds, part of his revolutionary geometrization program...

their respective manifolds. Hyperbolic 3-manifold Hyperbolic space Hyperbolization theorem Margulis lemma Normally hyperbolic invariant manifold Kapovich...

turn into 3-manifold theory. The JSJ decomposition and Thurston's hyperbolization theorem reduces the study of knots in the 3-sphere to the study of various...

Gruyter, p. 294, ISBN 9783110808056. Otal, Jean-Pierre (2001), The hyperbolization theorem for fibered 3-manifolds, Contemporary Mathematics, vol. 7, American...

Tait flyping conjecture in 1991. Menasco, applying Thurston's hyperbolization theorem for Haken manifolds, showed that any prime, non-split alternating...

provides substantial shortcuts in modern proofs of Thurston's Hyperbolization Theorem for Haken 3-manifolds. Similarly, R-trees play a key role in the...

introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. Many knots were shown to be hyperbolic knots, enabling the use...

further into the mainstream. In the late 1970s William Thurston's hyperbolization theorem introduced the theory of hyperbolic 3-manifolds into knot theory...

the fact that any of these conjectures, combined with Thurston's hyperbolization theorem, would imply the geometrization conjecture. However, in practice...

Riemannian hyperbolization procedure developed by Ontaneda in a series of papers, which is a smooth version of the strict hyperbolization procedure introduced...

provides substantial shortcuts in modern proofs of Thurston's hyperbolization theorem for Haken 3-manifolds. Similarly, R {\displaystyle \mathbb {R}...

2018. Gallier, Jean; Xu, Dianna (2013). A Guide to the Classification Theorem for Compact Surfaces. Springer Science & Business Media. p. 156. ISBN 9783642343643...

work of Werner Israel, Brandon Carter, and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described...

also seemed to predict known massive particles as massless. Goldstone's theorem, relating to continuous symmetries within some theories, also appeared...

Fermat's Last Theorem, non-Euclidean geometry and the parallel postulate, the golden ratio, perfect numbers, the four color theorem, advocacy for duodecimal...

{m_{1}}{m_{2}}}\ .} Analogous to the inscribed angle theorem for circles one gets the Inscribed angle theorem for hyperbolas—For four points P i = ( x i , y...

behaves as if it were a Euclidean space. Fermi submitted his thesis, "A theorem on probability and some of its applications" (Un teorema di calcolo delle...

 'about diorismic theorems', which Halley translated as “de theorematis ad determinationem pertinentibus,” and Heath as “theorems involving determinations...

Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli (Theorems on the quadrature of the hyperbola, ellipse, and circle)...