Hodge numbers of a hypothetical complex structure on the six sphere. (English) Zbl 0996.53046

Ugarte, Luis

Geom. Dedicata 81, No. 1-3, 173-179 (2000).

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.

Reviewer: A.P.Stone (Albuquerque)

MSC:

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

Keywords:

complex structures; six-sphere; Hodge numbers; Frölicher spectral sequence