A vanishing identity on adjoint Reidemeister torsions of twist knots

Seokbeom Yoon

doi:10.2140/agt.2022.22.227

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arXiv · 2002.12576

A vanishing identity on adjoint Reidemeister torsions of twist knots

Seokbeom Yoon

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Abstract

For a compact oriented 3-manifold with torus boundary the adjoint Reidemeister torsion is defined as a function on the $\mathrm{SL}_2(\mathbb{C})$-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 identities. In this paper, we prove that the conjecture holds for all hyperbolic twist knot exteriors by using Jacobi's residue theorem.

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Seokbeom Yoon. 2020-02-28. A vanishing identity on adjoint Reidemeister torsions of twist knots. https://doi.org/10.2140/agt.2022.22.227

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