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arXiv · 1710.07749

Conley conjecture and local Floer homology

Erman Cineli
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Abstract

In this paper we connect algebraic properties of the pair-of-pants product in local Floer homology and Hamiltonian dynamics. We show that for an isolated periodic orbit the product is non-uniformly nilpotent and use this fact to give a simple proof of the Conley conjecture for closed manifolds with aspherical symplectic form. More precisely, we prove that on a closed symplectic manifold the mean action spectrum of a Hamiltonian diffeomorphism with isolated periodic orbits is infinite.

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Erman Cineli. 2017-10-21. Conley conjecture and local Floer homology. https://doi.org/10.1007/s00013-018-1259-9

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