Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 2, pages 23-49.

A brief survey of the deformation theory of Kleinian groups

James W Anderson

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.

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

AMS subject classification. Primary: 30F40. Secondary: 57M50.

E-print: arXiv:math.GT/9810186

Submitted: 15 November 1997. Published: 23 October 1998.

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

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