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On the Lusternik–Schnirelmann category of Grassmannians

  • Israel Berstein (a1)

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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.

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References

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(1)Chern, S. S.On the multiplication in the characteristic ring of a sphere bundle. Ann. of Math (2) 49 (1948), 364–72.
(2)Grossmann, D. P.An estimation of the category of Lusternik–Schnirelmann. C.R. (Doklady). Sci. USSR 54 (1946), 109–12.
(3)Heinz, Hans-Peter and Singhof, Wilhelm. On Cup-length and Lusternik–Schnirelmann Category of Grassmann Manifolds. (To appear.)
(4)MacMahon, Percy A.Combinatory Analysis (Cambridge, 1915).
(5)Schwarz, A. S.The genus of a fibre space. Trudy Moscov. Mat. Obč. 11 (1967), 99126.

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