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Conilpotency and Weak Category

Published online by Cambridge University Press:  20 November 2018

C. S. Hoo
C. S. Hoo*
Affiliation:
University of Alberta, Edmonton, Alberta
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 730 - 734
Copyright
Copyright © Canadian Mathematical Society 1969

References

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