CLOSED GEODESIC LENGTHS IN HYPERBOLIC LINK COMPLEMENTS IN $S^3$

Abstract

Adams and Reid produced an upper bound for the length of a shortest closed geodesic in a hyperbolic knot or link complement in closed 3- manifolds which do not admit any Riemannian metric of negative curvature. We demonstrate that the length of an n th shortest closed geodesic in such manifolds is also bounded above for n > 1 and produce explicit upper bound on this length.