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Are the odd Betti numbers of an Almost-Kahler Einstein four manifolds necessarily even ?

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If some of Betti numbers were odd this would obviously contradict to Goldberg's conjecture, stating that Almost-Kahler Einstein manifolds are Kahler. I assume Goldberg's conjecture is open in all dimensions? –  Dmitri Mar 5 '11 at 10:19
Sorry for the double-retag. I think these tags should work. –  Elizabeth S. Q. Goodman Mar 5 '11 at 21:19

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