The topology of deformation spaces of Kleinian groups

dc.creatorAnderson, James W.
dc.creatorCanary, Richard D.
dc.creatorMcCullough, Darryl
dc.date1998-06-13
dc.date2000-11-01
dc.date.accessioned2026-07-07T05:25:03Z
dc.date.available2026-07-07T05:25:03Z
dc.descriptionLet M be a compact, hyperbolizable 3-manifold with nonempty incompressible boundary and let AH(π_1(M)) denote the space of (conjugacy classes of) discrete faithful representations of π_1(M) into PSL 2 (C). The components of the interior MP(π_1(M)) of AH(π_1(M)) (as a subset of the appropriate representation variety) are enumerated by the space A(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(π_1(M)) and hence a conjectural topological enumeration of the components of AH(π_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(π_1(M)) has infinitely many components.
dc.description49 pages, published version
dc.identifierhttps://arxiv.org/abs/math/9806079
dc.identifierhttp://arxiv.org/abs/math/9806079
dc.identifierAnn. of Math. (2) 152 (2000), no. 3, 693--741
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77043
dc.subjectGeometric Topology
dc.titleThe topology of deformation spaces of Kleinian groups
dc.typetext

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