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arXiv · 2103.08221

The Gopakumar-Vafa finiteness conjecture

Aleksander Doan·Eleny-Nicoleta Ionel·Thomas Walpuski
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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.

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Aleksander Doan, Eleny-Nicoleta Ionel, Thomas Walpuski. 2021-03-15. The Gopakumar-Vafa finiteness conjecture. https://arxiv.org/abs/2103.08221

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