1-loop equals torsion for two-bridge knots

Abstract

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