Super-representations of 3-manifolds and torsion polynomials
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929278385389568 |
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| author | Garoufalidis, Stavros Yoon, Seokbeom |
| author_facet | Garoufalidis, Stavros Yoon, Seokbeom |
| contents | Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that involves edges as well as faces, we associate a polynomial to a cusped hyperbolic manifold that conjecturally agrees with the $\BC^2$-torsion polynomial, which conjecturally detects the genus of the knot. The new combinatorics is motivated by super-geometry in dimension 3, and more precisely by super-Ptolemy assignments of ideally triangulated 3-manifolds and their $\mathrm{OSp}_{2|1}(\BC)$-representations. Extended section 4, and added superalgebras with a single odd generator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11018 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Super-representations of 3-manifolds and torsion polynomials Garoufalidis, Stavros Yoon, Seokbeom Geometric Topology High Energy Physics - Theory Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that involves edges as well as faces, we associate a polynomial to a cusped hyperbolic manifold that conjecturally agrees with the $\BC^2$-torsion polynomial, which conjecturally detects the genus of the knot. The new combinatorics is motivated by super-geometry in dimension 3, and more precisely by super-Ptolemy assignments of ideally triangulated 3-manifolds and their $\mathrm{OSp}_{2|1}(\BC)$-representations. Extended section 4, and added superalgebras with a single odd generator. |
| title | Super-representations of 3-manifolds and torsion polynomials |
| topic | Geometric Topology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2301.11018 |