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The study of algebraic properties of groups of transformations of a manifoldgives rise to an interplay between different areas of mathemathics such astopology, geometry, and dynamical systems. Especially, in this paper, we pointout some interplays between topology, geometry, and dynamical systems which areunderlying to the group of symplectic homeomorphisms. The latter situation canoccur when one thinks of the following question. Is there a flux geometry whichis underlying to the group of strong symplectic homeomorphisms so that Fathi'sPoincare duality theorem continues to hold? We discuss on some possible answersof the above preoccupation, and we elaborate various topological analogues ofsome well-known results found in the field of symplectic dynamics. We leaveseveral open questions and conjectures.

An enlargement of some symplectic objects