Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914000959176704 |
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| author | Yeral, Deniz |
| author_facet | Yeral, Deniz |
| contents | For a ribbon fusion category $\mathcal{A}$ and a special symmetric commutative Frobenius algebra $F$ in $\mathcal{A}$, we use factorization homology and the ansular correlators obtained via the modular microcosm principle to construct a diffeomorphism invariant vector inside the skein module of any closed oriented three-dimensional manifold. If $\mathcal{A}$ is a modular fusion category and $F$ is the monoidal unit, this recovers the Reshetikhin-Turaev invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants Yeral, Deniz Quantum Algebra For a ribbon fusion category $\mathcal{A}$ and a special symmetric commutative Frobenius algebra $F$ in $\mathcal{A}$, we use factorization homology and the ansular correlators obtained via the modular microcosm principle to construct a diffeomorphism invariant vector inside the skein module of any closed oriented three-dimensional manifold. If $\mathcal{A}$ is a modular fusion category and $F$ is the monoidal unit, this recovers the Reshetikhin-Turaev invariants. |
| title | Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2508.16351 |