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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.

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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