Quantum Steenrod squares and the equivariant pair-of-pants in symplectic cohomology

Abstract

We relate the quantum Steenrod square to Seidel’s equivariant pair-of-pants product for open convex symplectic manifolds that are either monotone or exact, using an equivariant version of the PSS isomorphism. We define continuation maps between different Hamiltonians in [Formula: see text]-equivariant Floer cohomology, and prove expected properties of them. We prove a symplectic Cartan relation for the equivariant pair-of-pants product, pointing out the difficulties in stating it. We give a nonvanishing result for the equivariant pair-of-pants product for some elements of [Formula: see text]. We finish by calculating the symplectic square for the negative line bundles [Formula: see text], proving an equivariant version of a result due to Ritter.