Non left-orderable surgeries on negatively twisted torus knots

TL;DR

This paper identifies specific negatively twisted torus knots for which certain Dehn surgeries produce 3-manifolds with non left-orderable fundamental groups, expanding understanding of the relationship between knot surgeries and group orderability.

Contribution

It demonstrates that some negatively twisted torus knots admit surgeries resulting in non left-orderable fundamental groups, a novel connection in knot theory and 3-manifold topology.

Findings

Certain negatively twisted torus knots admit non left-orderable surgeries.

Dehn surgeries on these knots produce 3-manifolds with non left-orderable fundamental groups.

The work links knot surgery properties to algebraic orderability of fundamental groups.

Abstract

We show that certain negatively twisted torus knots admit Dehn surgeries yielding 3-manifolds with non left-orderable fundamental groups.