Short geodesics in hyperbolic 3–manifolds

For each $g \geq 2$ , 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 $S$ .

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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

Volume 11, issue 2 (2011)

William Breslin

Abstract