The equivariant pair-of-pants product in fixed point Floer cohomology

TL;DR

This paper introduces an equivariant pair-of-pants product in fixed point Floer cohomology to establish a Smith-type inequality, extending previous results with a new approach.

Contribution

It develops an equivariant version of the pair-of-pants product in Floer cohomology and proves a Smith-type inequality using this new framework.

Findings

Established a Smith-type inequality for Floer cohomology groups.

Introduced an equivariant pair-of-pants product for symplectic automorphisms.

Extended previous results with a novel method.

Abstract

The Floer cohomology of a symplectic automorphism and that of its square are related by the pair-of-pants product. For exact symplectic automorphisms, we introduce an equivariant version of that product, and use it to prove a Smith-type inequality of ranks between Floer cohomology groups. Under additional topological assumptions, the same inequality was previously proved by Hendricks, using a different strategy.