Left-orderability and exceptional Dehn surgery on twist knots

TL;DR

This paper proves that all non-trivial exceptional Dehn surgeries on twist knots, except the trefoil, produce 3-manifolds with left-orderable fundamental groups, supporting a broader conjecture in 3-manifold topology.

Contribution

It generalizes previous results by showing left-orderability for a wider class of Dehn surgeries on twist knots, excluding only the trefoil case.

Findings

Exceptional non-trivial Dehn surgeries on twist knots (except trefoil) have left-orderable fundamental groups.

Supports the conjecture linking left-orderability and Dehn surgery types.

Extends prior work by Clay, Lidman, and Watson to a broader class of knots.

Abstract

We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a 3-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.