C0–Symplectic Geometry Under Displacements

ABSTRACT This paper continues the study of the group Hameo(M, ω), of all Hamiltonian homeomorphisms of a closed symplectic manifold (M, ω). After given a direct proof of the positivity result of the symplectic displacement energy, we show that the uniqueness theorem of generators of strong symplectic isotopies extends to any closed symplectic manifold: An explicit formula for the mass flow of any strong symplectic isotopy with respect to its generator is given. We show that Hameo(M, ω) inherits under the C0 -Hamiltonian topology, the fragmentation property, the algebraic perfectness, and coincides with the commutator sub-group of the group of all strong symplectic homeomorphisms. This solves a Banyaga's conjecture, and some other conjectures are also formulated.