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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.

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