#### Volume 14, issue 6 (2014)

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Towards the $C^0$ flux conjecture

### Lev Buhovsky

Algebraic & Geometric Topology 14 (2014) 3493–3508
##### Abstract

In this note, we generalise a result of Lalonde, McDuff and Polterovich concerning the ${C}^{0}$ flux conjecture, thus confirming the conjecture in new cases of symplectic manifolds. We also prove the continuity of the flux homomorphism on the space of smooth symplectic isotopies endowed with the ${C}^{0}$ topology, which implies the ${C}^{0}$ rigidity of Hamiltonian paths, conjectured by Seyfaddini.

##### Keywords
symplectic manifold, Hamiltonian diffeomorphism, symplectomorphism, $C^0$ flux conjecture, flux homomorphism
Primary: 57R17