The Gopakumar-Vafa formula for symplectic manifolds
Symplectic Geometry
2017-10-10 v6 Algebraic Geometry
Abstract
The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. Using the methods of symplectic Gromov-Witten theory, we prove that the Gopakumar-Vafa formula holds for any symplectic Calabi-Yau 6-manifold, and hence for Calabi-Yau 3-folds. The results extend to all symplectic 6-manifolds and to the genus zero GW invariants of semipositive manifolds.
Cite
@article{arxiv.1306.1516,
title = {The Gopakumar-Vafa formula for symplectic manifolds},
author = {Eleny-Nicoleta Ionel and Thomas H. Parker},
journal= {arXiv preprint arXiv:1306.1516},
year = {2017}
}
Comments
We have clarified the analytic setting by adding further details to Sections 4 and 5 and expanding the appendix, which now parts A and B. To appear in Annals of Mathematics