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Hodge numbers of a hypothetical complex structure on the six sphere. (English) Zbl 0996.53046
From author’s abstract: The author proves that the terms $$E_r^{p,q} (S^6)$$ in the Frölicher spectral sequence associated to any hypothetical complex structure on $$S^6$$ would satisfy Serre duality. It is also shown that the vanishing of the Dolbeault cohomology group $$H^{1,1}(S^6)$$ ensures the existence of a holomorphic 2-form on $$S^6$$ living even in $$E^{2,0}_2 (S^6)$$, which in particular implies the nondegeneration of Frölicher’s sequence at the second level.

##### MSC:
 53C56 Other complex differential geometry 55T99 Spectral sequences in algebraic topology 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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