Atlas: Hyperbolic Dehn Surgery and Algebraic Convergence For Kleinian Groups by Timothy D. Comar

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The 1996 Joint Spring Topology Conference and Southeast Dynamical Systems Conference
March 7-9, 1996
Ball State University
Muncie, IN, USA

Organizers
John Emert, Kerry Jones, Roger Nelson

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Hyperbolic Dehn Surgery and Algebraic Convergence For Kleinian Groups
by
Timothy D. Comar
University of Michigan

Let M be a compact three-manifold with boundary containing k (greater than or equal to 1) tori. Assume that the interior of M is homeomorphic to H³ / \Gamma, where \Gamma is a nonelementary, torsion-free geometrically finite Kleinian group with the property that each parabolic element of \Gamma is conjugate into one of k rank two parabolic subgroups corresponding to the tori. We show that the interiors of most manifolds obtained from M by Dehn filling admit geometrically finite hyperbolic structures that are geometrically close to H³ / \Gamma.

We use the above result to obtain a general recipe for constructing examples of convergent sequences of discrete, faithful representations \phi_n: \Gamma' --> PSL(2, C) of a group \Gamma' whose algebraic limits are properly contained in their geometric limits.

Date received: January 11, 1996