Shrinkwrapping and the taming of hyperbolic 3-manifolds : preprint

By Danny Calegari, David Gabai. 2004

303 citations recorded by the source corpus.

We introduce a new technique for finding CAT(-1) surfaces in hyperbolic 3-manifolds. We use this to show that a complete hyperbolic 3-manifold with finitely generated fundamental group is geometrically and topologically tame.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d56b4c90482eb938cdeebe9a60692a12adc67e8a

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In Computer Graphics and Computer-Aided Design

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Twisted cohomology for hyperbolic three manifolds (2010, unknown): “This is equivalent to say that π1(M) is finitely generated, by the proof of Marden’s conjecture [1, 8].”
Two-generator free Kleinian groups and hyperbolic displacements (2009, background): “Proof By the conclusions of Propositions 6.9 and 3.9 in [8] and tameness ([1], [5]) every Γ –invariant D –conformal density M is a constant multiple of the area density A , i.e., D = 2.”
The classification of Kleinian surface groups I : Models and bounds : preprint (2003, background): “When this article was originally written the question of tameness was still open, but it has since been resolved by Agol [2] and CalegariGabai [21].”
KLEINIAN GROUPS IN HIGHER DIMENSIONS (2007, unknown): “Gabai [48] in the general case.”
3-Manifold Groups (2012, background): “ear groups: they are residually ﬁnite [Hem87], they satisfy the Tits Alternative (see (C.20) and (K.2) below), etc. (5) The solutions to Marden’s Tameness Conjecture by Agol [Ag07] and Calegari–Gabai [CaG06], combined with Canary’s Covering Theorem [Cay96] implies the Subgroup Tameness Theorem (see ”
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-proper Settings (2014, background): “Moreover, the recent resolution of the Ahlfors measure conjecture [2, 41] has more to do with threedimensional topology than with analysis and dynamics.”
Realising end invariants by limits of minimally parabolic, geometrically finite groups (2005, background): “Then the simple loop conjecture proved by Gabai [25] gives us an essential simple closed curve c on ∂C such that p(c) inessential on Σ′ ∪ P ′′.”