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A brief survey of the deformation theory of Kleinian groups. (English) Zbl 0904.30024

Rivin, Igor (ed.) et al., The Epstein Birthday Schrift dedicated to David Epstein on the occasion of his 60th birthday. Warwick: University of Warwick, Institute of Mathematics, Geom. Topol. Monogr. 1, 23-49 (1998).
Summary: 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.
For the entire collection see [Zbl 0901.00063].

MSC:

30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
57M50 General geometric structures on low-dimensional manifolds
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