On the Flux Conjectures

Lalonde, Francois; McDuff, Dusa; Polterovich, Leonid

On the Flux Conjectures

Authors

Lalonde, Francois

McDuff, Dusa

Polterovich, Leonid

Description

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.
Latex, 21 pages