On the Flux Conjectures
dg-ga
2008-02-03 v1 Differential Geometry
Abstract
The ``Flux conjecture'' for symplectic manifolds states that the group of Hamiltonian diffeomorphisms is C^1-closed in the group of all symplectic diffeomorphisms. We prove the conjecture for spherically rational manifolds and for those whose minimal Chern number on 2-spheres either vanishes or is large enough. We also confirm a natural version of the Flux conjecture for symplectic torus actions. In some cases we can go further and prove that the group of Hamiltonian diffeomorphisms is C^0-closed in the identity component of the group of all symplectic diffeomorphisms.
Cite
@article{arxiv.dg-ga/9706015,
title = {On the Flux Conjectures},
author = {Francois Lalonde and Dusa McDuff and Leonid Polterovich},
journal= {arXiv preprint arXiv:dg-ga/9706015},
year = {2008}
}
Comments
Latex, 21 pages