Presymplectic geometry and Liouville sectors with corners and its monoidality
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912621240778752 |
|---|---|
| author | Oh, Yong-Geun |
| author_facet | Oh, Yong-Geun |
| contents | We provide a presymplectic characterization of Liouville sectors introduced by Ganatra-Pardon-Shende in terms of the characteristic foliation of the boundary, which we call Liouville $σ$-sectors. We extend this definition to the case with corners using the presymplectic geometry of null foliations of the coisotropic intersections of transverse coisotropic collection of hypersurfaces which appear in the definition of Liouville sectors with corners. We show that the set of Liouville $σ$-sectors with corners canonically forms a monoid which provides a natural framework of considering the Künneth-type functors in the wrapped Fukaya category. We identify its automorphism group which enables one to give a natural definition of bundles of Liouville sectors. As a byproduct, we affirmatively answer to a question raised in Question 2.6 in [GPS20], which asks about the optimality of their definition of Liouville sectors [GPS20]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_11726 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Presymplectic geometry and Liouville sectors with corners and its monoidality Oh, Yong-Geun Symplectic Geometry 53D40, 53D05 We provide a presymplectic characterization of Liouville sectors introduced by Ganatra-Pardon-Shende in terms of the characteristic foliation of the boundary, which we call Liouville $σ$-sectors. We extend this definition to the case with corners using the presymplectic geometry of null foliations of the coisotropic intersections of transverse coisotropic collection of hypersurfaces which appear in the definition of Liouville sectors with corners. We show that the set of Liouville $σ$-sectors with corners canonically forms a monoid which provides a natural framework of considering the Künneth-type functors in the wrapped Fukaya category. We identify its automorphism group which enables one to give a natural definition of bundles of Liouville sectors. As a byproduct, we affirmatively answer to a question raised in Question 2.6 in [GPS20], which asks about the optimality of their definition of Liouville sectors [GPS20]. |
| title | Presymplectic geometry and Liouville sectors with corners and its monoidality |
| topic | Symplectic Geometry 53D40, 53D05 |
| url | https://arxiv.org/abs/2110.11726 |