Algebraic & Geometric Topology

Left-orderability and cyclic branched coverings

Ying Hu

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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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 399-413.

Dates
Received: 3 February 2014
Revised: 25 June 2014
Accepted: 30 June 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840916

Digital Object Identifier
doi:10.2140/agt.2015.15.399

Mathematical Reviews number (MathSciNet)
MR3325741

Zentralblatt MATH identifier
1312.57001

Subjects
Primary: 57M05: Fundamental group, presentations, free differential calculus
Secondary: 57M12: Special coverings, e.g. branched 57M27: Invariants of knots and 3-manifolds

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

Citation

Hu, Ying. Left-orderability and cyclic branched coverings. Algebr. Geom. Topol. 15 (2015), no. 1, 399--413. doi:10.2140/agt.2015.15.399. https://projecteuclid.org/euclid.agt/1510840916


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