Towards the C0 flux conjecture

Buhovsky, Lev

doi:10.2140/agt.2014.14.3493

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Towards the $C^0$ flux conjecture

Lev Buhovsky

Algebraic & Geometric Topology 14 (2014) 3493–3508

DOI: 10.2140/agt.2014.14.3493

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

Mathematical Subject Classification 2010

Primary: 57R17

References

Publication

Received: 16 September 2013

Revised: 12 April 2014

Accepted: 6 May 2014

Published: 15 January 2015

Authors

Lev Buhovsky
School of Mathematical Sciences Tel Aviv University Ramat Aviv 69978 Tel Aviv Israel
http://www.math.tau.ac.il/~levbuh/

Volume 14, issue 6 (2014)