C^0 Lagrangian Monodromy

Abstract: We prove that (under appropriate orientation assumptions), the action of a Hamiltonian homeomorphism \phi on the cohomology of a relatively exact Lagrangian fixed by \phi 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 \phi on relative cohomology.