The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates
arXiv:2110.11003 · doi:10.1007/s00209-024-03491-y
Abstract
We present an alternative definition of the twisted 1-loop invariant in terms of the Jacobian of Ptolemy coordinates. As an application, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This implies that the 1-loop conjecture proposed by Dimofte and Garoufalidis holds for all hyperbolic once-punctured torus bundles.