Mutation and SL(2,C)-Reidemeister torsion for hyperbolic knots

TL;DR

This paper proves that the SL(2,C)-Reidemeister torsion of hyperbolic knots remains invariant under mutation along Conway spheres, highlighting a topological invariant's stability under specific knot transformations.

Contribution

It establishes the invariance of the SL(2,C)-Reidemeister torsion for hyperbolic knots under mutation, a previously unproven property.

Findings

Reidemeister torsion is invariant under mutation along Conway spheres.

The invariance applies to any lift of the holonomy to SL(2,C).

The result enhances understanding of knot invariants in hyperbolic geometry.

Abstract

Given a hyperbolic knot, we prove that the Reidemeister torsion of any lift of the holonomy to SL(2,C) is invariant under mutation along a Conway sphere.