The topology of deformation spaces of Kleinian groups
| dc.creator | Anderson, James W. | |
| dc.creator | Canary, Richard D. | |
| dc.creator | McCullough, Darryl | |
| dc.date | 1998-06-13 | |
| dc.date | 2000-11-01 | |
| dc.date.accessioned | 2026-07-07T05:25:03Z | |
| dc.date.available | 2026-07-07T05:25:03Z | |
| dc.description | Let 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.description | 49 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/9806079 | |
| dc.identifier | http://arxiv.org/abs/math/9806079 | |
| dc.identifier | Ann. of Math. (2) 152 (2000), no. 3, 693--741 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77043 | |
| dc.subject | Geometric Topology | |
| dc.title | The topology of deformation spaces of Kleinian groups | |
| dc.type | text |