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The mod ℭ Suspension Theorem

Published online by Cambridge University Press:  20 November 2018

Benson Samuel Brown
Benson Samuel Brown*
Affiliation:
Sir George Williams University, Montreal, Quebec
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Our aim in this paper is to prove the general mod ℭ suspension theorem: Suppose that X and Y are CW-complexes,ℭ is a class offinite abelian groups, and that

(i) πi(Y) ∈ℭfor all i < n,

(ii) H*(X; Z) is finitely generated,

(iii) Hi(X;Z) ∈ℭfor all i > k.

Then the suspension homomorphism

is a(mod ℭ) monomorphism for 2 ≦ r ≦ 2n – k – 2 (when r= 1, ker E is a finite group of order d, where Zd∈ ℭ and is a (mod ℭ) epimorphism for 2 ≦ r ≦ 2n – k – 2

The proof is basically the same as the proof of the regular suspension theorem. It depends essentially on (mod ℭ) versions of the Serre exact sequence and of the Whitehead theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 684 - 701
Copyright
Copyright © Canadian Mathematical Society 1969

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