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arXiv:1307.1919 [math.GT]AbstractReferencesReviewsResources

Systoles and Dehn surgery for hyperbolic 3-manifolds

Grant S. Lakeland, Christopher J. Leininger

Published 2013-07-07, updated 2013-10-29Version 2

Given a closed hyperbolic 3-manifold M of volume V, and a link L in 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 non-compact finite volume hyperbolic manifold which grows asymptotically like (4/3)log(V).

Comments: 15 pages, 2 figures. Corrected an error and adjusted main statements; made minor edits
Categories: math.GT
Subjects: 57M50
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