English

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

R2 v1 2026-06-21T23:26:18.682Z