### References & Citations

# Mathematics > Geometric Topology

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

(Submitted on 21 Oct 2021)

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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