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Non-degenerescence of some spectral sequences

K. S. Sarkaria (1984)

Annales de l'institut Fourier

Each Lie algebra of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold M définies, in a natural way, a spectral sequence E k ( ) which converges to the de Rham cohomology of M in a finite number of steps. We prove e.g. that for all k 0 there exists a foliated compact manifold with E k ( ) infinite dimensional.

On some spaces which are covered by a product space

Izu Vaisman (1977)

Annales de l'institut Fourier

In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the...

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