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A brief survey of the deformation theory of Kleinian groups

A brief survey of the deformation theory of Kleinian groups
A brief survey of the deformation theory of Kleinian groups
We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion of the parametrization by topological data of the components of the closure of the deformation space; the relationship between algebraic and geometric limits of sequences of Kleinian groups; and the behavior of several geometrically and analytically interesting functions on the deformation space.
kleinian group, deformation space, hyperbolic manifold, algebraic limits, geometric limits, strong limits
23-49
Geometry & Topology Publications
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Rivin, Igor
Rourke, Colin
Series, Caroline
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Rivin, Igor
Rourke, Colin
Series, Caroline

Anderson, James W. (1998) A brief survey of the deformation theory of Kleinian groups. In, Rivin, Igor, Rourke, Colin and Series, Caroline (eds.) The Epstein Birthday Schrift. (Geometry & Topology Monographs, 1) Coventry, UK. Geometry & Topology Publications, pp. 23-49. (doi:10.2140/gtm.1998.1.23).

Record type: Book Section

Abstract

We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion of the parametrization by topological data of the components of the closure of the deformation space; the relationship between algebraic and geometric limits of sequences of Kleinian groups; and the behavior of several geometrically and analytically interesting functions on the deformation space.

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More information

Published date: 1998
Additional Information: ISSN 1464-8989
Keywords: kleinian group, deformation space, hyperbolic manifold, algebraic limits, geometric limits, strong limits

Identifiers

Local EPrints ID: 29870
URI: http://eprints.soton.ac.uk/id/eprint/29870
PURE UUID: 7ff8c827-f231-4b59-98d2-353fdd23c4ef
ORCID for James W. Anderson: ORCID iD orcid.org/0000-0002-7849-144X

Catalogue record

Date deposited: 17 May 2007
Last modified: 16 Mar 2024 02:52

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Contributors

Editor: Igor Rivin
Editor: Colin Rourke
Editor: Caroline Series

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