Some results of Hamiltonian homeomorphism on aspherical closed surfaces.
Max Planck Institute for Mathematics in the Sciences
On closed symplectically aspherical manifolds, Schwarz proved a
classical result that the action function of a nontrivial Hamiltonian
diffeomorphism is not constant by using Floer homology. In this talk,
we will show how to generalize Schwarz`s theorem to the $C^0$-case
on closed aspherical surfaces. As application, we prove that the
contractible fixed points set (and consequently the fixed points set)
of a nontrivial Hamiltonian homeomorphism is not connected.