1994•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

Non-simple geodesics in hyperbolic 3-manifolds

Kerry N. Jones, Alan W. Reid

Abstract

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.

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Key concepts: Geodesic, Simple (philosophy), Mathematics, Hyperbolic 3-manifold, Geodesic map, Hyperbolic manifold, Pure mathematics, Set (abstract data type)