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• W2121073874 abstract "Let M be a compact, hyperbolizable 3-manifold with nonempty incompressible boundary and let AH(…1(M)) denote the space of (conjugacy classes of) discrete faithful representations of …1(M )i nto PSL 2(C). The components of the interior MP(…1(M)) of AH(…1(M)) (as a subset of the appropriate representation variety) are enumerated by the spaceA(M) of marked homeomorphism types of oriented, compact, irreducible 3-manifolds homotopy equivalent to M. In this paper, we give a topological enumeration of the components of the closure of MP(…1(M)) and hence a conjectural topological enumeration of the components of AH(…1(M)). 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(…1(M)) has inflnitely many components. In this paper, we begin a study of the global topology of deformation spaces of Kleinian groups. The basic object of study is the space AH(…1(M)) of marked hyperbolic 3-manifolds homotopy equivalent to a flxed compact 3manifold M. The interior MP(…1(M)) of AH(…1(M)) is very well understood due to work of Ahlfors, Bers, Kra, Marden, Maskit, Sullivan and Thurston. In particular, the components ofMP(…1(M)) are enumerated by topological data, namely the set A(M) of marked, compact, oriented, irreducible 3-manifolds homotopy equivalent to M, while each component is parametrized by analytic data coming from the conformal boundaries of the hyperbolic 3-manifolds. Thurston’s Ending Lamination Conjecture provides a conjectural classiflcation for elements of AH(…1(M)) by data which are partially topologi" @default.
• W2121073874 created "2016-06-24" @default.
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• W2121073874 date "2000-11-01" @default.
• W2121073874 modified "2023-10-16" @default.
• W2121073874 title "The Topology of Deformation Spaces of Kleinian Groups" @default.
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• W2121073874 doi "https://doi.org/10.2307/2661352" @default.
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