Volume 11, issue 2 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Short geodesics in hyperbolic $3$–manifolds

William Breslin

Algebraic & Geometric Topology 11 (2011) 735–745
Abstract

For each g 2, we prove existence of a computable constant ϵ(g) > 0 such that if S is a strongly irreducible Heegaard surface of genus g in a complete hyperbolic 3–manifold M and γ is a simple geodesic of length less than ϵ(g) in M, then γ is isotopic into S.

Keywords
Heegaard surface, hyperbolic $3$–manifold, geodesic
Mathematical Subject Classification 2000
Primary: 57M50
References
Publication
Received: 24 May 2010
Revised: 14 January 2011
Accepted: 15 January 2011
Published: 12 March 2011
Authors
William Breslin
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor MI 48109-1043
USA
http://www-personal.umich.edu/~breslin/index.html