Left-orderability and cyclic branched coverings
Geometric Topology
2015-05-27 v3
Abstract
We provide an alternative proof of a sufficient condition for the fundamental group of the cyclic branched cover of along a prime knot to be left-orderable, which is originally due to Boyer-Gordon-Watson. As an application of this sufficient condition, we show that for any two-bridge knot, with , there are only finitely many cyclic branched covers whose fundamental groups are not left-orderable. This answers a question posed by D{\c a}bkowski, Przytycki and Togha.
Cite
@article{arxiv.1311.3291,
title = {Left-orderability and cyclic branched coverings},
author = {Ying Hu},
journal= {arXiv preprint arXiv:1311.3291},
year = {2015}
}
Comments
13 pages, 2 figures; the abstract and introduction are substantially revised from the previous version; a mathematical typo is corrected in section 4;