The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908877266616320 |
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| author | Garoufalidis, Stavros Yoon, Seokbeom |
| author_facet | Garoufalidis, Stavros Yoon, Seokbeom |
| contents | We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formulas for the Alexander polynomial and its variants, the twisted Alexander polynomial and the $L^2$-Alexander torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds Garoufalidis, Stavros Yoon, Seokbeom Geometric Topology High Energy Physics - Theory We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formulas for the Alexander polynomial and its variants, the twisted Alexander polynomial and the $L^2$-Alexander torsion. |
| title | The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds |
| topic | Geometric Topology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.01536 |