#### Volume 14, issue 3 (2014)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Systoles and Dehn surgery for hyperbolic $3$–manifolds

### Grant S Lakeland and Christopher J Leininger

Algebraic & Geometric Topology 14 (2014) 1441–1460
##### Abstract

Given a closed hyperbolic $3$–manifold $M$ of volume $V$, and a link $L\subset M$ such that the complement $M\setminus L$ is hyperbolic, we establish a bound for the systole length of $M\setminus L$ 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 $7.35534\dots$ As part of the proof, we establish a bound for the systole length of a noncompact finite volume hyperbolic manifold which grows asymptotically like $\frac{4}{3}logV$.

##### Keywords
systole, Kleinian group, isometric sphere
Primary: 57M50
##### Publication
Revised: 29 October 2013
Accepted: 5 November 2013
Published: 7 April 2014
##### Authors
 Grant S Lakeland Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green St 273 Altgeld Hall Urbana, IL 61801 USA Christopher J Leininger Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green St 273 Altgeld Hall Urbana, IL 61801 USA