A natural Gromov-Witten virtual fundamental class
Symplectic Geometry
2015-10-19 v3
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.
Keywords
Cite
@article{arxiv.1302.3472,
title = {A natural Gromov-Witten virtual fundamental class},
author = {Eleny-Nicoleta Ionel and Thomas H. Parker},
journal= {arXiv preprint arXiv:1302.3472},
year = {2015}
}
Comments
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