Non left-orderable surgeries and generalized Baumslag-Solitar relators

TL;DR

This paper identifies conditions under which certain knot surgeries result in non left-orderable groups, focusing on knots with generalized Baumslag-Solitar relators and applying this to specific twisted torus knots.

Contribution

It introduces new criteria linking generalized Baumslag-Solitar relators in knot groups to non left-orderable surgeries, expanding understanding of knot group orderability.

Findings

Certain knots with generalized Baumslag-Solitar relators have non left-orderable surgeries.

Positively twisted torus knots can admit non left-orderable surgeries under these conditions.

The paper provides new methods to identify non left-orderable 3-manifold groups.

Abstract

We show that a knot has a non left-orderable surgery if the knot group admits a generalized Baumslag-Solitar relator and satisfies certain conditions on a longitude of the knot. As an application, it is shown that certain positively twisted torus knots admit non left-orderable surgeries.