1-loop equals torsion for fibered 3-manifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909442557083648 |
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| author | Dunfield, Nathan M. Garoufalidis, Stavros Yoon, Seokbeom |
| author_facet | Dunfield, Nathan M. Garoufalidis, Stavros Yoon, Seokbeom |
| contents | In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to be equal to the $\mathbb{C}^2$ and the $\mathbb{C}^3$-torsion polynomials. Here, we prove this conjecture for layered triangulations of fibered 3-manifolds with toroidal boundary, and we illustrate our theorems with exact computations of the 1-loop and the torsion polynomials. As further evidence for the conjecture, we confirm it for more than 6,600 nonfibered manifolds, and use this data to explore the extent to which the $\mathbb{C}^2$-torsion determines the Thurston norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00469 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 1-loop equals torsion for fibered 3-manifolds Dunfield, Nathan M. Garoufalidis, Stavros Yoon, Seokbeom Geometric Topology High Energy Physics - Theory 57K31, 57K32 In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to be equal to the $\mathbb{C}^2$ and the $\mathbb{C}^3$-torsion polynomials. Here, we prove this conjecture for layered triangulations of fibered 3-manifolds with toroidal boundary, and we illustrate our theorems with exact computations of the 1-loop and the torsion polynomials. As further evidence for the conjecture, we confirm it for more than 6,600 nonfibered manifolds, and use this data to explore the extent to which the $\mathbb{C}^2$-torsion determines the Thurston norm. |
| title | 1-loop equals torsion for fibered 3-manifolds |
| topic | Geometric Topology High Energy Physics - Theory 57K31, 57K32 |
| url | https://arxiv.org/abs/2304.00469 |