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.

中文翻译：

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关于迭代哈密顿Floer同调

本文的重点是在辛非球面流形上哈密顿量的滤波和局部 Floer 同调迭代下的行为。迭代哈密顿量的 Floer 同调带有自然循环群作用。在过滤的情况下，我们表明该动作的生成器的超迹等于未迭代哈密顿量的同调的欧拉特征。对于局部同调，超迹是不动点的 Lefschetz 指数。我们还证明了迭代局部同调和这些结果的等变版本的经典 Smith 不等式的模拟。