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A vanishing identity of adjoint Reidemeister torsions of twist knots

Seokbeom Yoon

Algebraic & Geometric Topology 22 (2022) 227–249
Abstract

For a compact oriented 3–manifold with torus boundary, the adjoint Reidemeister torsion is defined as a function on the SL 2()–character variety, depending on a choice of a boundary curve. Under reasonable assumptions, it is conjectured that the adjoint torsion satisfies a certain type of vanishing identity. We prove that the conjecture holds for all hyperbolic twist knot exteriors by using Jacobi’s residue theorem.

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Keywords
adjoint Reidemeister torsion, twist knot, residue theorem
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 6 March 2020
Revised: 7 December 2020
Accepted: 23 February 2021
Published: 26 April 2022
Authors
Seokbeom Yoon
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Barcelona
Spain