# Equivariant Lagrangian Floer cohomology via semi-global Kuranishi structures

## TL;DR

This paper introduces a new approach to defining equivariant Lagrangian Floer cohomology using semi-global Kuranishi structures, simplifying previous perturbation methods for fixed Lagrangian pairs under finite symplectic group actions.

## Contribution

It develops a simplified Kuranishi perturbation framework to define equivariant Floer cohomology for symmetric Lagrangian pairs, advancing computational and theoretical understanding.

## Key findings

- Provides a new definition of equivariant Floer cohomology
- Simplifies Kuranishi perturbation theory for symplectic geometry
- Enables computations for fixed Lagrangian submanifolds under group actions

## Abstract

Using a simplified version of Kuranishi perturbation theory that we call semi-global Kuranishi structures, we give a definition of the equivariant Lagrangian Floer cohomology of a pair of Lagrangian submanifolds that are fixed under a finite symplectic group action and satisfy certain simplifying assumptions.