Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915403972739072 |
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| author | Ulmer, Jakob |
| author_facet | Ulmer, Jakob |
| contents | Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invariants. We explain how the open-closed morphism is an ingredient towards quantizing the large $N$ open SFT of an object of a Calabi-Yau category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism Ulmer, Jakob Quantum Algebra Mathematical Physics Algebraic Topology Symplectic Geometry 53D37, 81T70, 53D45, 16E40 Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invariants. We explain how the open-closed morphism is an ingredient towards quantizing the large $N$ open SFT of an object of a Calabi-Yau category. |
| title | Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism |
| topic | Quantum Algebra Mathematical Physics Algebraic Topology Symplectic Geometry 53D37, 81T70, 53D45, 16E40 |
| url | https://arxiv.org/abs/2507.15445 |