On the iterated Hamiltonian Floer homology

The focus of the paper is the behavior under iterations of the filtered and local Floer homology of a Hamiltonian on a symplectically aspherical manifold. The Floer homology of an iterated Hamiltonian comes with a natural cyclic group action. In the filtered case, we show that the supertrace of a generator of this action is equal to the Euler characteristic of the homology of the un-iterated Hamiltonian. For the local homology the supertrace is the Lefschetz index of the fixed point. We also prove an analog of the classical Smith inequality for the iterated local homology and the equivariant versions of these results.

Automated summary

This paper focuses on the behavior under iterations of the filtered and local Floer homology of a Hamiltonian on a symplectically aspherical manifold. The authors prove that the supertrace of a generator of the cyclic group action on the filtered Floer homology is equal to the Euler characteristic of the un-iterated Hamiltonian's homology. They also establish the Lefschetz index of fixed points in the local homology, and analogs of the classical Smith inequality for iterated local homology and equivariant versions of these results.