Simple Closed Geodesics in Hyperbolic 3-Manifolds

Details Simple Closed Geodesics in Hyperbolic 3-Manifolds Simple Closed Geodesics in Hyperbolic 3-Manifolds

1998-01-14

arxiv.org/abs/math/9801071v1

Mathematics

Geometric Topology

7 pages, to appear in the Bulletin of the London Mathematical Society

Scientific paper

This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete non-elementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite or that it has finitely generated fundamental group.

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