Hamiltonian isotopies of relatively exact Lagrangians are orientation-preserving

2023/08/26 by Smith, Jack
#53D12 #53D40 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2401.03356

Abstract

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.

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