A vanishing identity of adjoint Reidemeister torsions of twist knots

Yoon, Seokbeom

doi:10.2140/agt.2022.22.227

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A vanishing identity of adjoint Reidemeister torsions of twist knots

Seokbeom Yoon

Algebraic & Geometric Topology 22 (2022) 227–249

DOI: 10.2140/agt.2022.22.227

Abstract

For a compact oriented $3$ –manifold with torus boundary, the adjoint Reidemeister torsion is defined as a function on the ${SL}_{2} (ℂ)$ –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

Volume 22, issue 1 (2022)