Connections on equivariant Hamiltonian Floer cohomology

TL;DR

This paper introduces a method to differentiate $S^1$-equivariant Hamiltonian Floer cohomology with respect to formal parameters, expanding the analytical tools available in symplectic topology.

Contribution

It constructs connections on equivariant Floer cohomology that enable differentiation with respect to formal parameters, a novel analytical development.

Findings

Established a new connection framework for equivariant Floer cohomology

Enabled differentiation with respect to formal parameters in Floer theory

Potential applications in symplectic topology and Hamiltonian dynamics

Abstract

We construct connections on $S^1$-equivariant Hamiltonian Floer cohomology, which differentiate with respect to certain formal parameters.