Volume 14, issue 3 (2014)

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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 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 logV .

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