Open 2D TFTs admit initial open-closed extensions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915578457882624 |
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| author | Barkan, Shaul Steinebrunner, Jan Zhang, Adela YiYu |
| author_facet | Barkan, Shaul Steinebrunner, Jan Zhang, Adela YiYu |
| contents | We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology object of its value at the disk. As a corollary, we obtain an action of the moduli spaces of surfaces on the Hochschild homology object of $E_1$-Calabi-Yau algebras. This provides a space level refinement of previous work of Costello over $\mathbb{Q}$ and Wahl-Westerland and Wahl over $\mathbb{Z}$, and serves as a crucial ingredient to Lurie's "non-compact cobordism hypothesis" in dimension 2. As part of the proof we also give a description of slice categories of the d-dimensional bordism category with boundary, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Open 2D TFTs admit initial open-closed extensions Barkan, Shaul Steinebrunner, Jan Zhang, Adela YiYu Algebraic Topology Category Theory Geometric Topology 57K20, 16E40, 81T40, 18M05, 58D10 We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology object of its value at the disk. As a corollary, we obtain an action of the moduli spaces of surfaces on the Hochschild homology object of $E_1$-Calabi-Yau algebras. This provides a space level refinement of previous work of Costello over $\mathbb{Q}$ and Wahl-Westerland and Wahl over $\mathbb{Z}$, and serves as a crucial ingredient to Lurie's "non-compact cobordism hypothesis" in dimension 2. As part of the proof we also give a description of slice categories of the d-dimensional bordism category with boundary, which may be of independent interest. |
| title | Open 2D TFTs admit initial open-closed extensions |
| topic | Algebraic Topology Category Theory Geometric Topology 57K20, 16E40, 81T40, 18M05, 58D10 |
| url | https://arxiv.org/abs/2509.02553 |