Hyperbolic Manifolds and Discrete Groups

By Michael Kapovich. 2000

563 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5ab9b50254a52b4ac810d1c6af067becdb434778

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In Geometry and Topology

Citations in the corpus

Twisted cohomology for hyperbolic three manifolds (2010, unknown): “The ﬁrst one can be found in standard references about Kleinian groups (cf. [18]): Lemma 3.3.”
Universal bounds for hyperbolic Dehn surgery (2002, methodology): “By Thurston’s Geometrization Theorem for Haken manifolds ([45], [37], [38], [29]), N supports a complete, finite volume metric of constant negative curvature.”
Three-Dimensional Orbifolds and Their Geometric Structures (2003, methodology): “Kapovich’s book [120], using Rips theory.”
THE DEFORMATION SPACES OF CONVEX RP²-STRUCTURES ON 2-ORBIFOLDS (2001, background): “See also Ratcliffe [34], Bridson-Haefliger [3], and Kapovich [25].”
Contact Anosov flows on hyperbolic 3–manifolds (2013, background): “6 (Hyperbolization Theorem, Thurston [50], Kapovich [37], Otal [43]) The interior of a compact atoroidal Haken 3–manifold with torus boundary admits a complete hyperbolic Riemannian metric (that is, with sectional curvature 1) of finite volume.”
Geometry and rigidity of mapping class groups (2008, background): “n to Rn for constants K′,C′ that depend only on K,C,s. Now any (K′,C′)-quasi-isometric embedding from Rn into Rn is a (K′,C′′)-quasi-isometry where C′′ depends only on K′,C′, and n; see, for example, [34]. It follows that π is uniformly onto, meaning that there exists a constant B depending only on ”
Geometric Group Theory (2018, methodology): “It is a corollary of Thurston’s Geometrization Theorem (see [Kap01]) that each Gromov–hyperbolic discrete subgroup of PO(3, 1) whose ideal boundary is homeomorphic to a Sierpinsky carpet is isomorphic to a round Sierpinsky carpet group.”
Deformations of reducible representations of 3–manifold groups into PSL2(ℂ) (2004, background): “It is easy to see that the tangent space to the orbit by conjugation corresponds to the space of 1-coboundaries B1(; sl2(C)ρ) (see for instance [ 15, Section 4.5 ]).”