Fully-Dualizable and Invertible $\mathcal{E}_n$-Algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908868789927936 |
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| author | Vazquez, Pablo Bustillo |
| author_facet | Vazquez, Pablo Bustillo |
| contents | We prove a conjecture of Brochier, Jordan, Safronov, and Snyder [BJSS21], first formulated by Lurie [Lur09b], characterizing fully-dualizable and invertible $\mathcal{E}_n$-algebras viewed as objects in the higher Morita categories $\mathbf{Mor}_n(\mathcal{V})$ [Lur09b, Sch14, Hau17b, Hau23]. In other words, we characterize those $\mathcal{E}_n$-algebras which give rise to $(n + 1)$-dimensional topological quantum field theories (TQFT), and those which give rise to invertible theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_05688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fully-Dualizable and Invertible $\mathcal{E}_n$-Algebras Vazquez, Pablo Bustillo Algebraic Topology Category Theory We prove a conjecture of Brochier, Jordan, Safronov, and Snyder [BJSS21], first formulated by Lurie [Lur09b], characterizing fully-dualizable and invertible $\mathcal{E}_n$-algebras viewed as objects in the higher Morita categories $\mathbf{Mor}_n(\mathcal{V})$ [Lur09b, Sch14, Hau17b, Hau23]. In other words, we characterize those $\mathcal{E}_n$-algebras which give rise to $(n + 1)$-dimensional topological quantum field theories (TQFT), and those which give rise to invertible theories. |
| title | Fully-Dualizable and Invertible $\mathcal{E}_n$-Algebras |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2603.05688 |