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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Convergence properties of end invariants

Jeffrey F Brock, Kenneth W Bromberg, Richard D Canary and Yair N Minsky

Geometry & Topology 17 (2013) 2877–2922
Abstract

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.

Keywords
Kleinian group, hyperbolic 3–manifold, end invariant, ending lamination
Mathematical Subject Classification 2010
Primary: 30F40, 57M50
References
Publication
Received: 23 August 2012
Revised: 16 January 2013
Accepted: 19 March 2013
Published: 14 October 2013
Proposed: David Gabai
Seconded: Benson Farb, Martin R Bridson
Authors
Jeffrey F Brock
Department of Mathematics
Brown University
Box 1917
Providence, RI 02912
USA
http://www.math.brown.edu/~brock/
Kenneth W Bromberg
Department of Mathematics
University of Utah
155 S 1400 E
Salt Lake City, UT 84112
USA
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
http://www.math.lsa.umich.edu/~canary
Yair N Minsky
Department of Mathematics
Yale University
10 Hillhouse Ave
PO Box 208283
New Haven, CT 06511
USA
http://www.math.yale.edu/users/yair