Left-orderability and exceptional Dehn surgery on two-bridge knots

TL;DR

This paper proves that exceptional non-trivial Dehn surgeries on hyperbolic two-bridge knots produce 3-manifolds with left-orderable fundamental groups, supporting a conjecture linking knot surgeries and orderability.

Contribution

It establishes a new class of 3-manifolds with left-orderable fundamental groups resulting from specific Dehn surgeries on two-bridge knots.

Findings

Exceptional non-trivial Dehn surgeries on hyperbolic two-bridge knots yield left-orderable fundamental groups

Supports the Boyer-Gordon-Watson conjecture relating Dehn surgery and orderability

Provides evidence for the broader relationship between knot theory and 3-manifold group properties

Abstract

We show that any exceptional non-trivial Dehn surgery on a hyperbolic two-bridge knot yields a 3-manifold whose fundamental group is left-orderable. This gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.