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arXiv · 2110.11003

The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates

Seokbeom Yoon
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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.

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Seokbeom Yoon. 2021-10-21. The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates. https://doi.org/10.1007/s00209-024-03491-y

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