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Abstract
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For a compact oriented
–manifold
with torus boundary, the adjoint Reidemeister torsion is defined as a function on the
–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
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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Publication
Received: 6 March 2020
Revised: 7 December 2020
Accepted: 23 February 2021
Published: 26 April 2022
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