Existence of ruled wrappings in hyperbolic 3–manifolds

Soma, Teruhiko

doi:10.2140/gt.2006.10.1173

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Existence of ruled wrappings in hyperbolic $3$–manifolds

Teruhiko Soma

Geometry & Topology 10 (2006) 1173–1184

DOI: 10.2140/gt.2006.10.1173

arXiv: 0903.0166

Abstract

We present a short elementary proof of an existence theorem of certain $CAT (- 1)$ –surfaces in open hyperbolic $3$ –manifolds. The main construction lemma in Calegari and Gabai’s proof of Marden’s Tameness Conjecture can be replaced by an applicable version of our theorem. Finally, we will give a short proof of the conjecture along their ideas.

Keywords

hyperbolic $3$–manifolds, ruled wrappings, Marden's tameness conjecture

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 30F40

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Publication

Received: 15 September 2004

Revised: 26 June 2006

Accepted: 8 July 2006

Published: 12 September 2006

Proposed: Jean-Pierre Otal

Seconded: David Gabai, Tobias Colding

Authors

Teruhiko Soma
Department of Mathematics and Information Sciences Tokyo Metropolitan University Minami-Ohsawa 1-1, Hachioji Tokyo 192-0397 Japan

Volume 10, issue 2 (2006)