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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(2, ) 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
References
Publication
Received: 20 September 2011
Revised: 27 September 2012
Accepted: 28 September 2012
Published: 31 October 2012
Authors
Pere Menal-Ferrer
Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Cerdanyola del Vallès
Spain
Joan Porti
Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Cerdanyola del Vallès
Spain
http://mat.uab.cat/~porti/