On the Flux Conjectures

Details On the Flux Conjectures On the Flux Conjectures

1997-06-26

arxiv.org/abs/dg-ga/9706015v1

Mathematics

Differential Geometry

Latex, 21 pages

Scientific paper

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.

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