Equivalence of the pearly tree immersed Lagrangian Floer theory and the Hamiltonian immersed Lagrangian Floer theory

TL;DR

This paper proves an equivalence between two approaches to immersed Lagrangian Floer theory, one using pearly tree discs and the other based on local Hamiltonian flows, extending previous work in the field.

Contribution

It establishes a general equivalence between pearly tree immersed Floer theory and Hamiltonian immersed Floer theory, broadening the understanding of their relationship.

Findings

Proves the equivalence between pearly tree and Hamiltonian Floer theories for immersed Lagrangians.

Generalizes previous results by Alston-Bao to a broader setting.

Provides a framework connecting geometric and Hamiltonian approaches in Floer theory.

Abstract

The goal of this paper is to prove an equivalence relation between the immersed Lagrangian Floer theory, defined using pearly tree discs, and local Hamiltonian flows, i.e., Hamiltonian flows performed in the Weinstein tubular neighborhood. This is a generalization of Alston-Bao's work.