Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links
Geometric Topology
2011-01-18 v2
Abstract
We consider closed orientable 3-dimensional hyperbolic manifolds which are cyclic branched coverings of the 3-sphere, with branching set being a two-bridge knot (or link). We establish two-sided linear bounds depending on the order of the covering for the Matveev complexity of the covering manifold. The lower estimate uses the hyperbolic volume and results of Cao-Meyerhoff and Gueritaud-Futer (who recently improved previous work of Lackenby), while the upper estimate is based on an explicit triangulation, which also allows us to give a bound on the Delzant T-invariant of the fundamental group of the manifold.
Keywords
Cite
@article{arxiv.math/0612830,
title = {Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links},
author = {Carlo Petronio and Andrei Vesnin},
journal= {arXiv preprint arXiv:math/0612830},
year = {2011}
}
Comments
Estimates improved using recent results of Gueritaud-Futer and Kim-Kim