English

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