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

Hakamata, Ryoto; Teragaito, Masakazu

doi:10.2140/agt.2014.14.2125

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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

DOI: 10.2140/agt.2014.14.2125

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

Volume 14, issue 4 (2014)