Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Non-simple geodesics in hyperbolic 3-manifolds

Kerry N. Jonesa1 and Alan W. Reida2*

a1 Ball State University, Muncie, IN 47306 U.S.A.

a2 Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge


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.

(Received May 24 1993)

(Revised November 05 1993)


* Supported in part by NSF DMS-9108050