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On the topology of deformation spaces of Kleinian groups

Anderson, James W., Canary, Richard D. and McCullough, Darryl (2000) On the topology of deformation spaces of Kleinian groups. Annals of Mathematics, 152 (3), 693-741.

Record type: Article

Abstract

Let M be a compact, hyperbolizable 3-manifold with nonempty incompressible boundary and fundamental group G, and let AH(G) denote the space of (conjugacy classes of) discrete faithful representations of G into PSL(2, C). The components of the interior MP(G) of AH(G) (as a subset of the appropriate representation variety) are enumerated by the space A(M) of marked homeomorphism types of oriented, compact, irreducible 3-manifolds homotopy equivalent to M. In this paper, we give a topological enumeration of the components of the closure of MP(G) and hence a conjectural topological enumeration of the components of AH(G). We do so by characterizing exactly which changes of marked homeomorphism type can occur in the algebraic limit of a sequence of isomorphic freely indecomposable Kleinian groups. We use this enumeration to exhibit manifolds M for which AH(G) has infinitely many components.

Text
topology_deformation.pdf - Author's Original

Published date: 2000

Identifiers

Local EPrints ID: 29872
URI: https://eprints.soton.ac.uk/id/eprint/29872
PURE UUID: fcc5b5a2-ebb4-4c17-83c7-549bdee6fa70
ORCID for James W. Anderson: orcid.org/0000-0002-7849-144X

Catalogue record

Date deposited: 20 Jul 2006

Contributors

Author: Richard D. Canary
Author: Darryl McCullough