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June 2012 The Conley conjecture for irrational symplectic manifolds
Doris Hein
J. Symplectic Geom. 10(2): 183-202 (June 2012).


We prove a generalization of the Conley conjecture: every Hamiltonian diffeomorphism of a closed symplectic manifold has infinitely many periodic orbits if the first Chern class vanishes over the second fundamental group. In particular, this removes the rationality condition from similar theorems by Ginzburg and Gürel. The proof in the irrational case involves several new ingredients including the definition and the properties of the filtered Floer homology for Hamiltonians on irrational manifolds. We also develop a method of localizing the filtered Floer homology for short action intervals using a direct sum decomposition, where one of the summands only depends on the behavior of the Hamiltonian in a fixed open set.


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Doris Hein. "The Conley conjecture for irrational symplectic manifolds." J. Symplectic Geom. 10 (2) 183 - 202, June 2012.


Published: June 2012
First available in Project Euclid: 7 June 2012

zbMATH: 1275.37026
MathSciNet: MR2926994

Rights: Copyright © 2012 International Press of Boston


Vol.10 • No. 2 • June 2012
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