Stiefel-Whitney characteristic classes and parallelizability of Grassmann manifolds. (English) Zbl 0566.57012

Bartík, Vojtěch; Korbaš, Július

Rend. Circ. Mat. Palermo, II. Ser., Suppl. 6, 19-29 (1984).

The authors present an independent and more elementary proof, showing directly that for any real Grassmann manifold, which is not diffeomorphic to projective space, its first or the second or the fourth Stiefel- Whitney characteristic class does not vanish. The Stiefel-Whitney characteristic classes from the first to the ninth are computed here in full generality. As a product of their method they obtain also some upper bounds for the span of Grassmannians, and they prove one non-embedding theorem.

Reviewer: G.Rassias

MSC:

57R20	Characteristic classes and numbers in differential topology
55R40	Homology of classifying spaces and characteristic classes in algebraic topology
57R40	Embeddings in differential topology

Keywords:

Grassmann manifold; Stiefel-Whitney characteristic class; non-embedding theorem