On left-orderable fundamental groups and Dehn surgeries on knots

TL;DR

This paper demonstrates that many manifolds obtained by specific Dehn surgeries on two-bridge knots have left-orderable fundamental groups, supporting a conjecture linking L-spaces and orderability.

Contribution

It provides new conditions under which Dehn surgeries on two-bridge knots produce manifolds with left-orderable fundamental groups, advancing understanding of the Boyer-Gordon-Watson conjecture.

Findings

Certain Dehn surgeries on two-bridge knots yield manifolds with left-orderable fundamental groups.

Supports the conjecture linking L-spaces and non-left-orderable fundamental groups.

Extends known classes of knots and surgeries satisfying the conjecture.

Abstract

We show that the resulting manifold by $r$-surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope $r$ satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer, Gordon and Watson that relates $L$-spaces and the left-orderability of their fundamental groups.