A homological criterion for the almost-existence of Hamiltonian chords

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.