Algebraic & Geometric Topology

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

Pere Menal-Ferrer and Joan Porti

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 4 (2012), 2049-2067.

Dates
Received: 20 September 2011
Revised: 27 September 2012
Accepted: 28 September 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715450

Digital Object Identifier
doi:10.2140/agt.2012.12.2049

Mathematical Reviews number (MathSciNet)
MR2994831

Zentralblatt MATH identifier
1271.57042

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
hyperbolic knot mutation Reidemeister torsion

Citation

Menal-Ferrer, Pere; Porti, Joan. Mutation and $\mathrm{SL}(2,\mathbb{C})$–Reidemeister torsion for hyperbolic knots. Algebr. Geom. Topol. 12 (2012), no. 4, 2049--2067. doi:10.2140/agt.2012.12.2049. https://projecteuclid.org/euclid.agt/1513715450


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