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l′-Isolated Maps and Localizations

Published online by Cambridge University Press:  20 November 2018

Sara Hurvitz
Sara Hurvitz*
Affiliation:
Bar-Ilan University, Ramat-Gan, Israel
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Let P be the set of primes, l ⊆ P a subset and l′ = P – l Recall that an H0-space is a space the rational cohomology of which is a free algebra.

Cassidy and Hilton defined and investigated l′-isolated homomorphisms between locally nilpotent groups. Zabrodsky [8] showed that if X and Y are simply connected H0-spaces either with a finite number of homotopy groups or with a finite number of homology groups, then every rational equivalence f : X → Y can be decomposed into an l-equivalence and an l′-equivalence.

In this paper we define and investigate l′-isolated maps between pointed spaces, which are of the homotopy type of path-connected nilpotent CW-complexes. Our definition of an l′-isolated map is analogous to the definition of an l′-isolated homomorphism. As every homomorphism can be decomposed into an l-isomorphism and an l′-isolated homomorphism, every map can be decomposed into an l-equivalence and an l′-isolated map.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 2 , 01 April 1983 , pp. 193 - 217
Copyright
Copyright © Canadian Mathematical Society 1983

References

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