Systoles and Dehn surgery for hyperbolic 3-manifolds
Geometric Topology
2014-10-01 v2
Abstract
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).
Keywords
Cite
@article{arxiv.1307.1919,
title = {Systoles and Dehn surgery for hyperbolic 3-manifolds},
author = {Grant S. Lakeland and Christopher J. Leininger},
journal= {arXiv preprint arXiv:1307.1919},
year = {2014}
}
Comments
15 pages, 2 figures. Corrected an error and adjusted main statements; made minor edits