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A brief survey of the deformation theory of Kleinian groups

James W Anderson

Geometry & Topology Monographs 1 (1998) 23–49

DOI: 10.2140/gtm.1998.1.23

arXiv: math.GT/9810186


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.

Dedicated to David Epstein on the occasion of his 60th birthday.


Kleinian group, deformation space, hyperbolic manifold, algebraic limits, geometric limits, strong limits

Mathematical Subject Classification

Primary: 30F40

Secondary: 57M50


Received: 15 November 1997
Revised: 28 August 1998
Published: 21 October 1998

James W Anderson
Faculty of Mathematical Studies
University of Southampton
SO17 1BJ