Equivariant Lagrangian Floer homology via multiplicative flow trees

TL;DR

This paper develops a new approach to equivariant Lagrangian Floer homology by constructing an $A_in$-module structure on the Floer complex, enabling advanced algebraic techniques in symplectic topology.

Contribution

It introduces a novel $A_in$-module framework for equivariant Floer homology, expanding the algebraic tools available for symplectic invariants.

Findings

Construction of equivariant Floer homology groups

Establishment of an $A_in$-module structure on Floer complexes

Potential applications to symplectic topology and mirror symmetry

Abstract

We provide constructions of equivariant Lagrangian Floer homology groups, by constructing and exploiting an $A_\infty$-module structure on the Floer complex.