Geodesic
l′-Isolated Maps and Localizations
Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 193-217

Voir la notice de l'article provenant de la source Cambridge University Press

Let P be the set of primes, l ⊆ P a subset and l′ = P – l Recall that an H 0-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 H 0-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. 
Hurvitz, Sara. l′-Isolated Maps and Localizations. Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 193-217. doi: 10.4153/CJM-1983-013-9
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