  The study of algebraic properties of groups of transformations of a manifold
gives rise to an interplay between different areas of mathemathics such as
topology, geometry, and dynamical systems. Especially, in this paper, we point
out some interplays between topology, geometry, and dynamical systems which are
underlying to the group of symplectic homeomorphisms. The latter situation can
occur when one thinks of the following question. Is there a flux geometry which
is underlying to the group of strong symplectic homeomorphisms so that Fathi's
Poincare duality theorem continues to hold? We discuss on some possible answers
of the above preoccupation, and we elaborate various topological analogues of
some well-known results found in the field of symplectic dynamics. We leave
several open questions and conjectures.
