Local topology in deformation spaces of hyperbolic 3–manifolds

Brock, Jeffrey F¹ ; Bromberg, Kenneth W² ; Canary, Richard D³ ; Minsky, Yair N⁴

¹ Department of Mathematics, Brown University, Box 1917, Providence RI 02912, USA
² Department of Mathematics, University of Utah, Salt Lake City UT 84112, USA
³ Department of Mathematics, University of Michigan, Ann Arbor, 2074 East Hall, 530 Church St, Ann Arbor MI 48109-1043, USA
⁴ Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven CT 06520-8283, USA

Geometry & topology, Tome 15 (2011) no. 2, pp. 1169-1224.

Résumé

We prove that the deformation space $AH\left(M\right)$ of marked hyperbolic $3$–manifolds homotopy equivalent to a fixed compact $3$–manifold $M$ 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 $3$–manifolds and Bers slices.

Détail

DOI : 10.2140/gt.2011.15.1169

Keywords: Kleinian group, hyperbolic $3$–manifold, deformation space, bumping

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