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September 2010 Local Floer homology and the action gap
Viktor L. Ginzburg, Başak Z. Gürel
J. Symplectic Geom. 8(3): 323-357 (September 2010).

Abstract

In this paper, we study the behavior of the local Floer homology of an isolated fixed point and the growth of the action gap under iterations. We prove that an isolated fixed point of a diffeomorphism remains isolated for the so-called admissible iterations and that the local Floer homology groups of a Hamiltonian diffeomorphism for such iterations are isomorphic to each other up to a shift of degree. Furthermore, we study the pair-of-pants product in local Floer homology, and characterize a particular class of isolated fixed points (the symplectically degenerate maxima), which plays an important role in the proof of the Conley conjecture. Finally, we apply these results to show that for a quasi-arithmetic sequence of admissible iterations of a Hamiltonian diffeomorphism with isolated fixed points the minimal action gap is bounded from above when the ambient manifold is closed and symplectically aspherical. This theorem is a generalization of the Conley conjecture.

Citation

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Viktor L. Ginzburg. Başak Z. Gürel. "Local Floer homology and the action gap." J. Symplectic Geom. 8 (3) 323 - 357, September 2010.

Information

Published: September 2010
First available in Project Euclid: 7 September 2010

zbMATH: 1206.53087
MathSciNet: MR2684510

Rights: Copyright © 2010 International Press of Boston

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Vol.8 • No. 3 • September 2010
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