Fukaya Algebra over $\mathbb{Z}$
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915580417671168 |
|---|---|
| author | Rabah, Mohamad |
| author_facet | Rabah, Mohamad |
| contents | Given a closed, connected, relatively-spin Lagrangian submanifold in a closed symplectic manifold, we associate to it a curved, gapped, filtered, $A_{n, K}$-algebra over the Novikov ring with integer coefficients. Under certain conditions, such an algebra can be extended to an $A_\infty$-algebra. To illustrate our framework, we give a proof of the Quantum Lefschetz Hyperplane Theorem in the K$\ddot a$hler case, and associate virtual fundamental classes to the moduli spaces used in local Gromov-Witten theory, in the symplectic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14657 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fukaya Algebra over $\mathbb{Z}$ Rabah, Mohamad Symplectic Geometry Given a closed, connected, relatively-spin Lagrangian submanifold in a closed symplectic manifold, we associate to it a curved, gapped, filtered, $A_{n, K}$-algebra over the Novikov ring with integer coefficients. Under certain conditions, such an algebra can be extended to an $A_\infty$-algebra. To illustrate our framework, we give a proof of the Quantum Lefschetz Hyperplane Theorem in the K$\ddot a$hler case, and associate virtual fundamental classes to the moduli spaces used in local Gromov-Witten theory, in the symplectic case. |
| title | Fukaya Algebra over $\mathbb{Z}$ |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2411.14657 |