Atlas: The topology of deformation spaces of hyperbolic 3-manifolds by Dick Canary

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G^3 = Geometric Groups on the Gulf coast
March 4-5, 2000
University of South Alabama
Mobile, AL, USA

Organizers
Phil Bowers, Stephen Brick, Jon Corson, Igor Mineyev

The topology of deformation spaces of hyperbolic 3-manifolds
by
Dick Canary
University of Michigan

One of the main objects of study in the field of Kleinian groups is the space AH(M) of all hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M. The interior of AH(M) has been well-understood since the 1970's. In particular, the components of the interior are enumerated by topological types of 3-manifolds homotopy equivalent to M and each component is naturally parameterized by analytic data. However, the remainder of the space is still somewhat mysterious.

We will survey some recent results on the global topology of AH(M).

Date received: February 8, 2000