Conilpotency and Weak Category

Hoo, C. S.

Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 730-734

Résumé

Let ƒ : X → Y be a map and let e′: Y → ΩΣY be the usual embedding. Then we prove the following results.Theorem 1. cat ƒ = cat(e′ƒ), w cat ƒ = w cat(e′ƒ) if Y is an H-space.Theorem 2. conil ƒ = w Σ cat(e′ƒ) ≦ Σ w cat(e′ƒ) ≦ w cat(e′ƒ), where Σ the suspension functor. If we take X = Y and ƒ= lx, this result yields conil X ≦ w cat e', a result due to Ganea, Hilton, and Peterson(4).Theorem 3. Suppose that Y is (m– 1)-connected and Then conil ƒ = w Σ cat (e′ƒ) = Σ w cat(e′ƒ) = w cat(e′ƒ).

Détail

DOI : 10.4153/CJM-1969-081-2

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