Volume 12, issue 4 (2012)

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Mutation and $\mathrm{SL}(2,\mathbb{C})$–Reidemeister torsion for hyperbolic knots

Pere Menal-Ferrer and Joan Porti

Algebraic & Geometric Topology 12 (2012) 2049–2067
Abstract

Given a hyperbolic knot, we prove that the Reidemeister torsion of any lift of the holonomy to $SL\left(2,ℂ\right)$ is invariant under mutation along a surface of genus 2, hence also under mutation along a Conway sphere.

Keywords
hyperbolic knot, mutation, Reidemeister torsion
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M50, 57M25