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

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

We reformulate the twisted 1-loop invariant in terms of Ptolemy coordinates. In addition, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This shows that the 1-loop conjecture proposed by Dimofte and Gar...

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Veröffentlicht in:Mathematische Zeitschrift 2024-05, Vol.307 (1), Article 19
1. Verfasser: Yoon, Seokbeom
Format: Artikel
Sprache:eng
Schlagworte:
Invariants
Mathematics
Mathematics and Statistics
Polynomials
Toruses
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Zusammenfassung:We reformulate the twisted 1-loop invariant in terms of Ptolemy coordinates. In addition, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This shows that the 1-loop conjecture proposed by Dimofte and Garoufalidis holds for all hyperbolic once-punctured torus bundles.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-024-03491-y