Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909188350803968 |
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| author | Smith, Jack |
| author_facet | Smith, Jack |
| contents | Given a closed, orientable Lagrangian submanifold $L$ in a symplectic manifold $(X, ω)$, we show that if $L$ is relatively exact then any Hamiltonian diffeomorphism preserving $L$ setwise must preserve its orientation. In contrast to previous results in this direction, there are no spin hypotheses on $L$. Curiously, the proof uses only mod-2 coefficients in its singular and Floer cohomology rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03356 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving Smith, Jack Symplectic Geometry 53D12, 53D40 Given a closed, orientable Lagrangian submanifold $L$ in a symplectic manifold $(X, ω)$, we show that if $L$ is relatively exact then any Hamiltonian diffeomorphism preserving $L$ setwise must preserve its orientation. In contrast to previous results in this direction, there are no spin hypotheses on $L$. Curiously, the proof uses only mod-2 coefficients in its singular and Floer cohomology rings. |
| title | Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving |
| topic | Symplectic Geometry 53D12, 53D40 |
| url | https://arxiv.org/abs/2401.03356 |