Journal of Symplectic Geometry

The Conley conjecture for irrational symplectic manifolds

Doris Hein

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Abstract

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.

Article information

Source
J. Symplectic Geom., Volume 10, Number 2 (2012), 183-202.

Dates
First available in Project Euclid: 7 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1339096434

Mathematical Reviews number (MathSciNet)
MR2926994

Zentralblatt MATH identifier
1275.37026

Citation

Hein, Doris. The Conley conjecture for irrational symplectic manifolds. J. Symplectic Geom. 10 (2012), no. 2, 183--202. https://projecteuclid.org/euclid.jsg/1339096434


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