#### 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.

Notes on file formats
James W Anderson

Faculty of Mathematical Studies

University of Southampton

Southampton, SO17 1BJ, England

Email: jwa@maths.soton.ac.uk

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