On the Lusternik–Schnirelmann category of Grassmannians

Author:

Berstein Israel

Abstract

This note contains a partial generalization of the results of (3). We extend to arbitrary n and k the complete determination of the cases in which cup length is strictly less than the maximum possible value dim Gn, k(R) = nk. We also show that the Lusternik–Schnirelmann category cat Gn, k(R) < nk in the same cases.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. The genus of a fibre space;Schwarz;Trudy Moscov. Mat. Obč.,1967

2. An estimation of the category of Lusternik–Schnirelmann;Grossmann;C.R. (Doklady). Sci. USSR,1946

3. (3) Heinz Hans-Peter and Singhof Wilhelm . On Cup-length and Lusternik–Schnirelmann Category of Grassmann Manifolds. (To appear.)

4. On the Multiplication in the Characteristic Ring of a Sphere Bundle

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