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

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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