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On the Stiefel-Whitney classes and the span of real Grassmannians. (English) Zbl 0622.57018
Continuing his previous research with V. Bártík [Rend. Circ. Mat. Palermo, II. Ser. 6, 19-29 (1984; Zbl 0566.57012)], the author first deduces the explicit formulae for the Stiefel-Whitney classes \(w_{10}\), \(w_{12}\), \(w_{14}\) and \(w_{16}\) of the Grassmann manifold \(G_{n,r}\) of all r-planes in a real n-space. This is applied for determining some further estimates for span \(G_{n,r}\), i.e. for the maximal number of linearly independent vector fields on \(G_{n,r}\).
Reviewer: I.Kolář

MSC:
57R25 Vector fields, frame fields in differential topology
57R20 Characteristic classes and numbers in differential topology
57T15 Homology and cohomology of homogeneous spaces of Lie groups
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