Convergence properties of end invariants

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, 155 S 1400 E, 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, PO Box 208283, New Haven, CT 06511, USA

Geometry & topology, Tome 17 (2013) no. 5, pp. 2877-2922.

Résumé

We prove a continuity property for ending invariants of convergent sequences of Kleinian surface groups. We also analyze the bounded curve sets of such groups and show that their projections to non-annular subsurfaces lie a bounded Hausdorff distance from geodesics joining the projections of the ending invariants.

Détail

DOI : 10.2140/gt.2013.17.2877

Classification : 30F40, 57M50
Keywords: Kleinian group, hyperbolic 3–manifold, end invariant, ending lamination

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