#### Volume 15, issue 1 (2015)

 Recent Issues
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Left-orderability and cyclic branched coverings

### Ying Hu

Algebraic & Geometric Topology 15 (2015) 399–413
##### Abstract

We provide an alternative proof of a sufficient condition for the fundamental group of the ${n}^{th}$ 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 $\left(p,q\right)$ 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 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