A simplicial construction of G-equivariant Floer homology

TL;DR

This paper introduces a new simplicial method to construct G-equivariant Floer cohomology for Lagrangian pairs on symplectic manifolds with Lie group actions, expanding the tools for symplectic topology.

Contribution

It develops a simplicial construction of G-equivariant Floer cohomology without relying on equivariant transversality assumptions.

Findings

Constructed G-equivariant Floer cohomology under specific hypotheses.

Provided a new framework for equivariant Floer theory.

Extended Floer homology to settings with Lie group symmetries.

Abstract

For G a Lie group acting on a symplectic manifold $(M,\omega)$ preserving a pair of Lagrangians $L_0$, $L_1$, under certain hypotheses not including equivariant transversality we construct a G-equivariant Floer cohomology of $L_0$ and $L_1$.