Local exotic tori
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912155344830464 |
|---|---|
| author | Brendel, Joé |
| author_facet | Brendel, Joé |
| contents | For a broad class of symplectic manifolds of dimension at least six, we find the following new phenomenon: there exist local exotic Lagrangian tori. More specifically, let $X$ be a geometrically bounded symplectic manifold of dimension at least six. We show that every open subset of $X$ contains infinitely many Lagrangian tori which are distinct up to symplectomorphisms of $X$ while being Lagrangian isotopic and having the same classical invariants. The proof relies on a locality property of the displacement energy germ, which allows us to compute it in a Darboux chart. Since these tori are not monotone, bubbling may occur and the count of Maslov index two $J$-holomorphic disks does not yield an invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11359 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local exotic tori Brendel, Joé Symplectic Geometry 53D12 (Primary) 53D20 (Secondary) For a broad class of symplectic manifolds of dimension at least six, we find the following new phenomenon: there exist local exotic Lagrangian tori. More specifically, let $X$ be a geometrically bounded symplectic manifold of dimension at least six. We show that every open subset of $X$ contains infinitely many Lagrangian tori which are distinct up to symplectomorphisms of $X$ while being Lagrangian isotopic and having the same classical invariants. The proof relies on a locality property of the displacement energy germ, which allows us to compute it in a Darboux chart. Since these tori are not monotone, bubbling may occur and the count of Maslov index two $J$-holomorphic disks does not yield an invariant. |
| title | Local exotic tori |
| topic | Symplectic Geometry 53D12 (Primary) 53D20 (Secondary) |
| url | https://arxiv.org/abs/2310.11359 |