The Gopakumar-Vafa formula for symplectic manifolds
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 C...
Veröffentlicht in: | Annals of Mathematics. - Dept. of Mathematics, Princeton University, 1884. - 187(2018), 1, Seite 1-64 |
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Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
2018
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Zugriff auf das übergeordnete Werk: | Annals of Mathematics |
Schlagworte: | Mathematics Physical sciences Philosophy |
Zusammenfassung: | 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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ISSN: | 0003486X |