A natural Gromov-Witten virtual fundamental class

Abstract

We describe a program for proving that the Gromov-Witten moduli spaces of compact symplectic manifolds carry a unique virtual fundamental class that satisfies certain naturality conditions. The virtual fundamental class is constructed using only Ruan-Tian perturbations by introducing stabilizing divisors, using Cech homology, and systematically applying naturality conditions. In high dimensions or low genus, no gluing theorems are needed.

35 pages, 2 figures. The main result in now restricted to high dimension or low genus; this corrects an error pointed out by M.Tehrani and A.Zinger, and uses their work in reference [TZ]. With this restriction, gluing theorems are not needed

References in corpus (2)

• Kuranishi homology and Kuranishi cohomology
• Kuranishi homology and Kuranishi cohomology: a User's Guide

Cited by in corpus (6)

• On Symplectic Sum Formulas in Gromov-Witten Theory
• Fukaya algebras via stabilizing divisors
• Geometric transversality in higher genus Gromov-Witten theory
• The Gromov-Witten axioms for symplectic manifolds via polyfold theory
• Automatic transversality in contact homology I: Regularity
• Limits of stable maps in a semi-stable degeneration