The Gopakumar-Vafa finiteness conjecture
Symplectic Geometry
2025-12-02 v2 Algebraic Geometry
Abstract
The Gopakumar-Vafa conjecture predicts that the BPS invariants of a symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are integers and all but finitely many vanish in every homology class. The integrality part of this conjecture was proved earlier by Ionel and Parker. This article proves the finiteness part. The proof relies on a modification of Ionel and Parker's cluster formalism using results from geometric measure theory.
Keywords
Cite
@article{arxiv.2103.08221,
title = {The Gopakumar-Vafa finiteness conjecture},
author = {Aleksander Doan and Eleny-Nicoleta Ionel and Thomas Walpuski},
journal= {arXiv preprint arXiv:2103.08221},
year = {2025}
}
Comments
v2: accepted for publication in Annals of Mathematics