An enlargement of some symplectic objects
Abstract
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.
Cite
@article{arxiv.1410.7891,
title = {An enlargement of some symplectic objects},
author = {Stéphane Tchuiaga},
journal= {arXiv preprint arXiv:1410.7891},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:0704.3194 by other authors