Open-closed Deligne-Mumford field theories: construction
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909014378414080 |
|---|---|
| author | Hirschi, Amanda Hugtenburg, Kai |
| author_facet | Hirschi, Amanda Hugtenburg, Kai |
| contents | Open-closed Deligne--Mumford field theories are chain-level field theories based on moduli spaces of stable curves with boundary. We associate to a relatively spin embedded Lagrangian $L \subset (X,ω)$ such an open-closed DMFT. It extends the Fukaya $A_\infty$ algebra to curves of arbitrarily high genus and with arbitrarily many boundary components and is unique up to homotopy. This is the first step in proving Kontsevich's conjecture that the Fukaya category determines the Gromov--Witten invariants of $X$, following a strategy delineated by Costello. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Open-closed Deligne-Mumford field theories: construction Hirschi, Amanda Hugtenburg, Kai Symplectic Geometry Algebraic Geometry Algebraic Topology 53D12, 53D45, 53D37, 81T40 Open-closed Deligne--Mumford field theories are chain-level field theories based on moduli spaces of stable curves with boundary. We associate to a relatively spin embedded Lagrangian $L \subset (X,ω)$ such an open-closed DMFT. It extends the Fukaya $A_\infty$ algebra to curves of arbitrarily high genus and with arbitrarily many boundary components and is unique up to homotopy. This is the first step in proving Kontsevich's conjecture that the Fukaya category determines the Gromov--Witten invariants of $X$, following a strategy delineated by Costello. |
| title | Open-closed Deligne-Mumford field theories: construction |
| topic | Symplectic Geometry Algebraic Geometry Algebraic Topology 53D12, 53D45, 53D37, 81T40 |
| url | https://arxiv.org/abs/2605.03521 |