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arXiv · 2401.03356

Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving

Jack Smith
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Abstract

Given a closed, orientable Lagrangian submanifold $L$ in a symplectic manifold $(X, \omega)$, 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.

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Jack Smith. 2023-08-26. Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving. https://arxiv.org/abs/2401.03356

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