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Conilpotency and Weak Category
Published online by Cambridge University Press: 20 November 2018
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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).
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- Copyright © Canadian Mathematical Society 1969
References
1.
Berstein, I. and Ganea, T., Homotopical nilpotency, Illinois J. Math.
5 (1961), 99–130.Google Scholar
2.
Berstein, I. and Hilton, P. J., Homomorphisms of homotopy structures, Topologie et géométrie différentielle, Séminaire Ehresmann, April, 1963 (Inst. Henri Poincaré, Paris, 1963).Google Scholar
3.
Ganea, T., On some numerical homotopy invariants, Proc. Internat. Congress Math., 1962, pp. 467–472 (Inst. Mittag-Leffler, Djursholm, Sweden, 1963).Google Scholar
4.
Ganea, T., Hilton, P. J., and Peterson, F. P., On the homotopy-commutativity of loop-spaces and suspensions, Topology
1 (1962), 133–141.Google Scholar
5.
Peterson, F. P., Numerical invariants of homotopy type, Colloquium on algebraic topology, pp. 79–83, Aarhus Universitet, 1962.Google Scholar
5.
Stasheff, J., On homotopy abelian H-spaces, Proc. Cambridge Philos. Soc.
57 (1961), 734–745.Google Scholar
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