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Left-orderable fundamental groups and Dehn surgery on genus one $2$–bridge knots

Ryoto Hakamata and Masakazu Teragaito

Algebraic & Geometric Topology 14 (2014) 2125–2148
Abstract
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For any hyperbolic genus-one 2–bridge knot in the 3–sphere, such as any hyperbolic twist knot, we show that the manifold resulting from r–surgery on the knot has left-orderable fundamental group if the slope r lies in some range, which depends on the knot.

Keywords
left-orderability, Dehn surgery, knot
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 06F15
References
Publication
Received: 26 December 2012
Revised: 14 November 2013
Accepted: 3 December 2013
Published: 28 August 2014
Authors
Ryoto Hakamata
Graduate School of Education
Hiroshima University
1-1-1 Kagamiyama
Higashi-hiroshima 739-8524
Japan
Masakazu Teragaito
Department of Mathematics and Mathematics Education
Hiroshima University
1-1-1 Kagamiyama
Higashi-hiroshima 739-8524
Japan