an:01505835
Zbl 0996.53046
Ugarte, Luis
Hodge numbers of a hypothetical complex structure on the six sphere
EN
Geom. Dedicata 81, No. 1-3, 173-179 (2000).
00066624
2000
j
53C56 55T99 53C15
complex structures; six-sphere; Hodge numbers; Fr??licher spectral sequence
From author's abstract: The author proves that the terms \(E_r^{p,q} (S^6)\) in the Fr??licher 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 Fr??licher's sequence at the second level.
A.P.Stone (Albuquerque)