Abstract:

In this paper, we define the $\mathbb{Z}/p$-equivariant product and coproduct maps in fixed point Floer cohomology. As applications, we obtain the Smith inequality for the $\mathbb{Z}/p$-action on the $p$-fold twisted loop space, which states that the rank of the Floer cohomology group $HF^*(\phi^p)$ is bounded below by that of $HF^*(\phi)$ for all prime $p.$ In particular, this generalizes the work of K. Hendricks and P. Seidel in the case of p=2.