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arXiv · 1306.1516

The Gopakumar-Vafa formula for symplectic manifolds

Eleny-Nicoleta Ionel·Thomas H. Parker
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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.

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BibTeXRIS

Eleny-Nicoleta Ionel, Thomas H. Parker. 2013-06-06. The Gopakumar-Vafa formula for symplectic manifolds. https://arxiv.org/abs/1306.1516

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