A homological criterion for the almost-existence of Hamiltonian chords

Antoine Rodrigues

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arXiv · 2511.02353

A homological criterion for the almost-existence of Hamiltonian chords

Antoine Rodrigues

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Abstract

We establish a criterion on wrapped Floer homology of an exact Lagrangian sub- manifold in a Liouville domain, which ensures the almost-existence of Hamiltonian chords near a given energy level. To this purpose we introduce a relative version of the coisotropic Hofer-Zehnder capacity, and compare it with some other capacities that are defined using filtered wrapped Floer homology. Our main application is the almost- existence of Hamiltonian chords near any hypersurface if the wrapped Floer homology vanishes.

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Antoine Rodrigues. 2025-11-04. A homological criterion for the almost-existence of Hamiltonian chords. https://arxiv.org/abs/2511.02353

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