On the topology of deformation spaces of Kleinian groups
James W. Anderson, Richard D. Canary,
and Darryl McCullough
Faculty of Mathematical Studies, University of
Southampton
Southampton, SO17 1BJ, England
Department of
Mathematics, University of Michigan, Ann Arbor, MI 48109
Department of Mathematics, University of Oklahoma, Norman, OK
73019
Abstract
Let M be a compact, hyperbolizable 3-manifold with nonempty
incompressible boundary and let AH(G) denote the space of
(conjugacy classes of) discrete fathful representations
of its fundamental group G into PSL2 (C).
The components of the interior MP(G)
of AH(G) (as a subset of the appropriate representation variety)
are enumerated by the space A(M) of
marked homeomorphism types of oriented, compact, irreducible
3-manifold homotopy equivalent to M.
In this paper, we give a topological enumeration of
the components of the closure of MP(G) and hence a conjectural
topological enumeration of the components of AH(G).
We do so by characterizing exactly
which changes of marked homeomorphism type can occur in the algebraic
limit of a sequence of isomorphic freely indecomposable Kleinian groups. We
use this enumeration to exhibit manifolds M for which
AH(G) has infinitely many components.
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On 27 Nov 1999, 12:14.