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Non-simple geodesics in hyperbolic 3-manifolds

Published online by Cambridge University Press:  24 October 2008

Kerry N. Jones  and
Alan W. Reid
Kerry N. Jones
Affiliation:
Ball State University, Muncie, IN 47306U.S.A.
Alan W. Reid
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge
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Abstract

Chinburg and Reid have recently constructed examples of hyperbolic 3-manifolds in which every closed geodesic is simple. These examples are constructed in a highly non-generic way and it is of interest to understand in the general case the geometry of and structure of the set of closed geodesics in hyperbolic 3-manifolds. For hyperbolic 3-manifolds which contain immersed totally geodesic surfaces there are always non-simple closed geodesics. Here we construct examples of manifolds with non-simple closed geodesics and no totally geodesic surfaces.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 2 , September 1994 , pp. 339 - 351
Copyright
Copyright © Cambridge Philosophical Society 1994

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