Volume 14, issue 4 (2014)

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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

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
Primary: 57M25
Secondary: 06F15