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Local topology in
deformation spaces of hyperbolic $3$–manifolds
Jeffrey F Brock, Kenneth W Bromberg, Richard D Canary and Yair N Minsky |
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Geometry & Topology 15 (2011) 1169–1224
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Abstract |
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We prove that the deformation space of marked hyperbolic –manifolds homotopy equivalent to a fixed compact –manifold with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar results are obtained for deformation spaces of acylindrical –manifolds and Bers slices. |
Keywords
Kleinian group, hyperbolic $3$–manifold, deformation space,
bumping
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Mathematical Subject Classification 2000
Primary: 30F40
Secondary: 57M50
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References |
Publication
Received: 12 November 2009
Accepted: 14 April 2011
Published: 26 July 2011
Proposed: Jean-Pierre Otal
Seconded: Benson Farb, Danny Calegari
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Authors |
| Jeffrey F Brock | |
| Department of Mathematics Brown University Box 1917 Providence RI 02912 USA |
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| http://www.math.brown.edu/~brock | |
| Kenneth W Bromberg | |
| Department of Mathematics University of Utah Salt Lake City UT 84112 USA |
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| http://www.math.utah.edu/~bromberg | |
| Richard D Canary | |
| Department of Mathematics University of Michigan, Ann Arbor 2074 East Hall 530 Church St Ann Arbor MI 48109-1043 USA |
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| http://www.math.lsa.umich.edu/~canary | |
| Yair N Minsky | |
| Department of Mathematics Yale University 10 Hillhouse Ave New Haven CT 06520-8283 USA |
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| http://www.math.yale.edu/users/yair | |
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