Are the odd-degree Betti numbers of a compact Almost-Kahler Einstein four manifold necessarily even ?
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2$\begingroup$ 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? $\endgroup$– Dmitri PanovMar 5, 2011 at 10:19
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1$\begingroup$ Sorry for the double-retag. I think these tags should work. $\endgroup$– Elizabeth S. Q. GoodmanMar 5, 2011 at 21:19
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1$\begingroup$ this is W. Watson's conjecture, which it seems is still open: facpub.stjohns.edu/~watsonw/diffgeom.htm (edited "odd" --> "odd-degree" to avoid a contradictio in terminis) $\endgroup$– Carlo BeenakkerSep 5, 2015 at 10:38
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