Left-orderability and cyclic branched coverings

Hu, Ying

doi:10.2140/agt.2015.15.399

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Left-orderability and cyclic branched coverings

Ying Hu

Algebraic & Geometric Topology 15 (2015) 399–413

DOI: 10.2140/agt.2015.15.399

Abstract

We provide an alternative proof of a sufficient condition for the fundamental group of the $n^{t h}$ cyclic branched cover of $S^{3}$ along a prime knot $K$ to be left-orderable, which is originally due to Boyer, Gordon and Watson. As an application of this sufficient condition, we show that for any $(p, q)$ two-bridge knot, with $p \equiv 3 mod 4$ , there are only finitely many cyclic branched covers whose fundamental groups are not left-orderable. This answers a question posed by Da̧bkowski, Przytycki and Togha.

Keywords

left-orderable groups, cyclic branched coverings, group representations, two-bridge knots, Riley's polynomial

Mathematical Subject Classification 2010

Primary: 57M05

Secondary: 57M12, 57M27

References

Publication

Received: 3 February 2014

Revised: 25 June 2014

Accepted: 30 June 2014

Published: 23 March 2015

Authors

Ying Hu
Department of Mathematics Louisiana State University Baton Rouge, LA 70803 USA
http://www.math.lsu.edu/~yhu4

Volume 15, issue 1 (2015)