A brief survey of the deformation theory of Kleinian groups

Details A brief survey of the deformation theory of Kleinian groups A brief survey of the deformation theory of Kleinian groups

1998-10-23

arxiv.org/abs/math/9810186v1

Geom. Topol. Monogr. 1 (1998), 23-49

Mathematics

Geometric Topology

27 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper2.abs.html

Scientific paper

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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