Behavior of the SU(2)-Reidemeister torsion form by mutation

TL;DR

This paper proves that the SU(2)-Reidemeister torsion form, associated with the knot exterior's character variety, remains unchanged under mutation along a Conway sphere, highlighting its topological invariance.

Contribution

It establishes the invariance of the twisted Reidemeister torsion form under mutation, a significant property in knot theory and 3-manifold topology.

Findings

Reidemeister torsion form is mutation-invariant

Invariance applies to the SU(2)-character variety of knot exteriors

Supports the topological robustness of the torsion form

Abstract

In this paper, we prove that the Reidemeister torsion twisted by the adjoint representation, which is considered as a 1-form, on the SU(2)-character variety of a knot exterior is invariant under mutation along a Conway sphere.