English

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.

Keywords

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

R2 v1 2026-07-22T12:30:07.159Z