Abstract.We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected CW-complexes, some of which extend /"-localization of nilpotent spaces, at a set of primes P. We focus our attention on one such functor, whose local objects are CW-complexes X for which the pth power map on the loop space QX is a self-homotopy equivalence if p & P. We study its algebraic properties, its behaviour on certain spaces, and its relation with other functors such as Bousfield's homology localization, Bousfield-Kan completion, and Quillen's plus-construction.
Abstract.We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected CW-complexes, some of which extend /"-localization of nilpotent spaces, at a set of primes P. We focus our attention on one such functor, whose local objects are CW-complexes X for which the pth power map on the loop space QX is a self-homotopy equivalence if p & P. We study its algebraic properties, its behaviour on certain spaces, and its relation with other functors such as Bousfield's homology localization, Bousfield-Kan completion, and Quillen's plus-construction.
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