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Strong convergence of Kleinian groups: the cracked eggshell

Strong convergence of Kleinian groups: the cracked eggshell
Strong convergence of Kleinian groups: the cracked eggshell
In this paper we give a complete description of the set of discrete faithful representations of the fundamental group of a compact, orientable, hyperbolizable 3-manifold M with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part of this description, we introduce coordinates on this set that extend the usual Ahlfors-Bers coordinates. We use these coordinates to show the local connectivity of this set and study the action of the modular group of M on this set.
0010-2571
1-37
Anderson, J.W.
739c0e33-ef61-4502-a675-575d08ee1a98
Lecuire, C.
675959b3-5107-461c-882d-40f4dd252fca
Anderson, J.W.
739c0e33-ef61-4502-a675-575d08ee1a98
Lecuire, C.
675959b3-5107-461c-882d-40f4dd252fca

Anderson, J.W. and Lecuire, C. (2010) Strong convergence of Kleinian groups: the cracked eggshell. Commentarii Mathematici Helvetici, n/a, 1-37. (doi:10.4171/CMH/304).

Record type: Article

Abstract

In this paper we give a complete description of the set of discrete faithful representations of the fundamental group of a compact, orientable, hyperbolizable 3-manifold M with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part of this description, we introduce coordinates on this set that extend the usual Ahlfors-Bers coordinates. We use these coordinates to show the local connectivity of this set and study the action of the modular group of M on this set.

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e-pub ahead of print date: 10 March 2010
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 73655
URI: https://eprints.soton.ac.uk/id/eprint/73655
ISSN: 0010-2571
PURE UUID: 113d9dc2-9435-4e26-8dcd-2b288c8a5f32
ORCID for J.W. Anderson: ORCID iD orcid.org/0000-0002-7849-144X

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Date deposited: 19 Mar 2010
Last modified: 06 Jun 2018 13:03

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