Systoles and Dehn surgery for hyperbolic 3-manifolds

Abstract

Given a closed hyperbolic 3-manifold M of volume V, and a link L ⊂ M such that the complement M \L is hyperbolic, we establish a bound for the systole length of M \L in terms of V. This extends a result of Adams and Reid, who showed that in the case that M is not hyperbolic, there is a universal bound of 7:35534::: As part of the proof, we establish a bound for the systole length of a noncompact finite volume hyperbolic manifold which grows asymptotically like 4/3 log V.