Homological Lagrangian monodromy for some monotone tori
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929337276563456 |
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| author | Augustynowicz, Marcin Smith, Jack Wornbard, Jakub |
| author_facet | Augustynowicz, Marcin Smith, Jack Wornbard, Jakub |
| contents | Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study of this group when $L$ is a monotone Lagrangian $n$-torus. Among other things, we describe $\mathcal{H}_L$ completely when $L$ is a monotone toric fibre, make significant progress towards classifying the groups than can occur for $n=2$, and make a conjecture for general $n$. Our classification results rely crucially on arithmetic properties of Floer cohomology rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_10507 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homological Lagrangian monodromy for some monotone tori Augustynowicz, Marcin Smith, Jack Wornbard, Jakub Symplectic Geometry 53D12, 53D40 Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study of this group when $L$ is a monotone Lagrangian $n$-torus. Among other things, we describe $\mathcal{H}_L$ completely when $L$ is a monotone toric fibre, make significant progress towards classifying the groups than can occur for $n=2$, and make a conjecture for general $n$. Our classification results rely crucially on arithmetic properties of Floer cohomology rings. |
| title | Homological Lagrangian monodromy for some monotone tori |
| topic | Symplectic Geometry 53D12, 53D40 |
| url | https://arxiv.org/abs/2201.10507 |