# name
Localizing with respect to self-maps of the circle

# metadata.dc.description.abstract[].value
We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected $ {\text{CW}}$-complexes, some of which extend $ P$-localization of nilpotent spaces, at a set of primes $ P$. We focus our attention on one such functor, whose local objects are $ {\text{CW}}$-complexes $ X$ for which the $ p$th power map on the loop space $ \Omega X$ is a self-homotopy equivalence if $ p \notin 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.

# metadata.dc.relation.ispartof[].value
Transactions of the American Mathematical Society, 1993, vol. 339, num. 1, p. 117-140

# metadata.dc.rights[].value
(c) American Mathematical Society (AMS), 1993

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Localizing with respect to self-maps of the circle