Non-left-orderable double branched coverings
Geometric Topology
2014-10-01 v3 Group Theory
Abstract
We develop a method to show the fundamental group of the double branched covering of a link is not left-orderable by introducing the notion of the coarse presentation. As in the usual group presentations, a coarse presentation is given by a set of generators and relations, but inequalities are allowed as relations. By using coarse presentation, we give a family of links whose double branched covering has the non-left-orderable fundamental group. Our family of links includes many known examples and new examples.
Cite
@article{arxiv.1106.1499,
title = {Non-left-orderable double branched coverings},
author = {Tetsuya Ito},
journal= {arXiv preprint arXiv:1106.1499},
year = {2014}
}
Comments
20 Pages, 11 figures; Errors in Theorem 3 and 4 are corrected