Equivalence between Gromov-Witten invariants: Domain dependent perturbation and Kuranishi structure approaches

TL;DR

This paper demonstrates the equivalence of two different methods for defining Gromov-Witten invariants, showing that domain-dependent perturbations and Kuranishi structures produce the same homology classes.

Contribution

It establishes the equivalence between the homology classes obtained from domain-dependent perturbations and Kuranishi structures in Gromov-Witten theory.

Findings

Homology classes from both approaches coincide.

Provides a rigorous proof of equivalence.

Bridges two major frameworks in symplectic geometry.

Abstract

We prove that the homology class induced by the rational pseudocycle constructed via domain-dependent perturbations by Cieliebak and Mohnke coincides with the homology class induced by the virtual fundamental class defined through Kuranishi structures by Fukaya, Oh, Ohta, and Ono.