January 2018 The Gopakumar-Vafa formula for symplectic manifolds
Eleny-Nicoleta Ionel, Thomas Parker
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Ann. of Math. (2) 187(1): 1-64 (January 2018). DOI: 10.4007/annals.2018.187.1.1

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 conjecture 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.

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Eleny-Nicoleta Ionel. Thomas Parker. "The Gopakumar-Vafa formula for symplectic manifolds." Ann. of Math. (2) 187 (1) 1 - 64, January 2018. https://doi.org/10.4007/annals.2018.187.1.1

Information

Published: January 2018
First available in Project Euclid: 23 December 2021

Digital Object Identifier: 10.4007/annals.2018.187.1.1

Subjects:
Primary: 53D45
Secondary: 14N35

Keywords: Gopakumar-Vafa conjecture , Gromov-Witten invariants , symplectic Calabi-Yau 3-folds

Rights: Copyright © 2018 Department of Mathematics, Princeton University

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Vol.187 • No. 1 • January 2018
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