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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.
Eleny-Nicoleta Ionel 1 ; Thomas H. Parker 2
@article{10_4007_annals_2018_187_1_1,
author = {Eleny-Nicoleta Ionel and Thomas H. Parker},
title = {The {Gopakumar-Vafa} formula for symplectic manifolds},
journal = {Annals of mathematics},
pages = {1--64},
publisher = {mathdoc},
volume = {187},
number = {1},
year = {2018},
doi = {10.4007/annals.2018.187.1.1},
mrnumber = {3739228},
zbl = {06841536},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.1.1/}
}
TY - JOUR AU - Eleny-Nicoleta Ionel AU - Thomas H. Parker TI - The Gopakumar-Vafa formula for symplectic manifolds JO - Annals of mathematics PY - 2018 SP - 1 EP - 64 VL - 187 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.1.1/ DO - 10.4007/annals.2018.187.1.1 LA - en ID - 10_4007_annals_2018_187_1_1 ER -
%0 Journal Article %A Eleny-Nicoleta Ionel %A Thomas H. Parker %T The Gopakumar-Vafa formula for symplectic manifolds %J Annals of mathematics %D 2018 %P 1-64 %V 187 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.1.1/ %R 10.4007/annals.2018.187.1.1 %G en %F 10_4007_annals_2018_187_1_1
Eleny-Nicoleta Ionel; Thomas H. Parker. The Gopakumar-Vafa formula for symplectic manifolds. Annals of mathematics, Tome 187 (2018) no. 1, pp. 1-64. doi: 10.4007/annals.2018.187.1.1
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