C0 Lagrangian Monodromy
Abstract
We prove that (under appropriate orientation assumptions), the action of a Hamiltonian homeomorphism φ on the cohomology of a relatively exact Lagrangian fixed by φ is the identity. This extends results of Hu-Lalonde-Leclercq and the author in the setting of Hamiltonian diffeomorphisms. We also prove a similar result regarding the action of φ on relative cohomology.
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