#### Volume 22, issue 1 (2022)

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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 ${\mathrm{SL}}_{2}\left(ℂ\right)$–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