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

2025/07/07 by Qin, Yuguo
#57R17 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2507.04798

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.

Citations

• Floer trajectories and stabilizing divisors
• Geometric transversality in higher genus Gromov-Witten theory
• A natural Gromov-Witten virtual fundamental class
• Technical details on Kuranishi structure and virtual fundamental chain
• Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory
• Symplectic hypersurfaces and transversality in Gromov-Witten theory
• Pseudocycles and Integral Homology
• Enumeration of rational curves via torus actions

Related

• Gromov-Witten theory via Kuranishi structures
• Gromov-Witten theory and invariants of matroids
• Pseudocycle Gromov-Witten invariants are a strict subset of polyfold Gromov-Witten invariants
• Partly-local domain-dependent almost complex structures
• K theoretic virtual fundamental cycle of global Kuranishi chart