Volume 15, issue 1 (2015)

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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 nth cyclic branched cover of S3 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 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