Geodesic
Left-orderability and cyclic branched coverings
Hu, Ying1
1Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 399-413
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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.

DOI : 10.2140/agt.2015.15.399
Classification : 57M05, 57M12, 57M27
Keywords: left-orderable groups, cyclic branched coverings, group representations, two-bridge knots, Riley's polynomial

Hu, Ying  1

1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA 
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Hu, Ying. Left-orderability and cyclic branched coverings. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 399-413. doi: 10.2140/agt.2015.15.399

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