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Simple Closed Geodesics in Hyperbolic 3-Manifolds
Published Web Locationhttps://arxiv.org/pdf/math/9801071.pdf
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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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