An edge-type state integral over local field and A-polynomials
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911788688211968 |
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| author | Fang, Honghuai |
| author_facet | Fang, Honghuai |
| contents | To each local field, Garoufalidis and Kashaev recently associate a quantum dilogarithm that satisfies a pentagon identity and some symmetries. By employing an angled version of these quantum dilogarithms, they developed three generalized TQFTs, one given by a face state-integral and others by edge state integrals. These TQFTs produce distributional invariants for one-cusped three-manifolds, which are believed to be related to counting points on the A-polynomial curve. In this paper, we will calculate partition functions of an edge-type generalized TQFT over a local field for several examples and prove the appearance of A-polynomial in these new invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An edge-type state integral over local field and A-polynomials Fang, Honghuai Quantum Algebra To each local field, Garoufalidis and Kashaev recently associate a quantum dilogarithm that satisfies a pentagon identity and some symmetries. By employing an angled version of these quantum dilogarithms, they developed three generalized TQFTs, one given by a face state-integral and others by edge state integrals. These TQFTs produce distributional invariants for one-cusped three-manifolds, which are believed to be related to counting points on the A-polynomial curve. In this paper, we will calculate partition functions of an edge-type generalized TQFT over a local field for several examples and prove the appearance of A-polynomial in these new invariants. |
| title | An edge-type state integral over local field and A-polynomials |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2403.02098 |