Systoles and Dehn surgery for hyperbolic 3–manifolds

Lakeland, Grant S; Leininger, Christopher J

doi:10.2140/agt.2014.14.1441

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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

DOI: 10.2140/agt.2014.14.1441

Abstract

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

Keywords

systole, Kleinian group, isometric sphere

Mathematical Subject Classification 2010

Primary: 57M50

References

Publication

Received: 15 July 2013

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

Volume 14, issue 3 (2014)