Vol. 37, No. 2, 1971

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Universal coefficient theorems for generalized homology and stable cohomotopy

Paul C. Kainen

Vol. 37 (1971), No. 2, 397–407
Abstract

We show that if h is a nice (e.g. representable) homology functor and G is an Abelian group, then there is a cohomology functor k(X;G) which is a “quasi-functor” of G and a short exact sequence

0 → Ext(h(ΣX ),G ) → k(X; G) → Hom (h(X),G) → 0

which is natural in X, “strongly quasi-natural” in G, and split if two additional conditions are satisfied.

Mathematical Subject Classification
Primary: 55J20
Milestones
Received: 23 October 1970
Revised: 24 February 1971
Published: 1 May 1971
Authors
Paul C. Kainen