The 3d-index of the 3d-skein module via the quantum trace map
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929377308049408 |
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| author | Garoufalidis, Stavros Yu, Tao |
| author_facet | Garoufalidis, Stavros Yu, Tao |
| contents | We define a map from the skein module of a cusped hyperbolic 3-manifold to the ring of Laurent series in one variable with integer coefficients that satisfies two properties: its evaluation at peripheral curves coincides with the Dimofte--Gaiotto--Gukov 3d-index, and it factors through the 3d-quantum trace map associated to a suitable ideal triangulation of the manifold. The map fulfills a supersymmetry prediction of mathematical physics and is part of a conjectural 3+1 dimensional topological quantum field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The 3d-index of the 3d-skein module via the quantum trace map Garoufalidis, Stavros Yu, Tao Geometric Topology High Energy Physics - Theory We define a map from the skein module of a cusped hyperbolic 3-manifold to the ring of Laurent series in one variable with integer coefficients that satisfies two properties: its evaluation at peripheral curves coincides with the Dimofte--Gaiotto--Gukov 3d-index, and it factors through the 3d-quantum trace map associated to a suitable ideal triangulation of the manifold. The map fulfills a supersymmetry prediction of mathematical physics and is part of a conjectural 3+1 dimensional topological quantum field theory. |
| title | The 3d-index of the 3d-skein module via the quantum trace map |
| topic | Geometric Topology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.04918 |