1-loop equals torsion for two-bridge knots

Stavros Garoufalidis; Seokbeom Yoon

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arXiv · 2411.03801

1-loop equals torsion for two-bridge knots

Stavros Garoufalidis·Seokbeom Yoon

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Abstract

Motivated by the conjectured asymptotics of the Kashaev invariant, Dimofte and the first author introduced a power series associated to a suitable ideal triangulation of a cusped hyperbolic 3-manifold, proved that its constant (1-loop) term is a topological invariant and conjectured that it equals to the adjoint Reidemeister torsion. We prove this conjecture for hyperbolic 2-bridge knots by combining the work of Ohtsuki--Takata with an explicit computation.

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Stavros Garoufalidis, Seokbeom Yoon. 2024-11-06. 1-loop equals torsion for two-bridge knots. https://arxiv.org/abs/2411.03801

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