English

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 nthn^{th} cyclic branched cover of S3S^3 along a prime knot KK to be left-orderable, which is originally due to Boyer-Gordon-Watson. As an application of this sufficient condition, we show that for any (p,q)(p,q) two-bridge knot, with p3 mod 4p\equiv 3 \text{ mod } 4, 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;

R2 v1 2026-06-22T02:07:02.953Z