The Gopakumar-Vafa formula for symplectic manifolds
By Eleny-Nicoleta Ionel, Thomas H. Parker. 2013
73 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c63d95367b76d1cc58904815b8636c02eeadb8de
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In Geometry and Topology
- Aaron Pixton
- R. Pandharipande
- A. Okounkov
- Davesh Maulik
- Yukinobu Toda
- Richard P. Thomas
- D. Oprea
- Jun Li
In Mathematical Physics
- Aaron Pixton
- R. Pandharipande
- A. Okounkov
- Davesh Maulik
- Richard P. Thomas
- Jun Li
- Yukinobu Toda
- D. Oprea
Citations in the corpus
- Gromov-Witten/pairs correspondence for the quintic 3-fold (2012, background): “of part (i) is slightly weaker than the full GopakumarVafapredicted BPS form, butbecomes equivalent withthevanishing assumed in (ii). A proof of the integrality of nX g,β has been recently claimed in [10]. The method is analytic but eventually reduces the integrality to the local curves calculation ”