The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914974694113280 |
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| author | Yoon, Seokbeom |
| author_facet | Yoon, Seokbeom |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_11003 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates Yoon, Seokbeom Geometric Topology High Energy Physics - Theory 57K31, 57K32 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. |
| title | The twisted 1-loop invariant and the Jacobian of Ptolemy coordinates |
| topic | Geometric Topology High Energy Physics - Theory 57K31, 57K32 |
| url | https://arxiv.org/abs/2110.11003 |