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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Localizing with respect to self-maps of the circle


Authors: Carles Casacuberta and Georg Peschke
Journal: Trans. Amer. Math. Soc. 339 (1993), 117-140
MSC: Primary 55P60; Secondary 18G99, 20J05, 55N25, 55P10
MathSciNet review: 1123451
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Abstract: 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1123451-X
PII: S 0002-9947(1993)1123451-X
Article copyright: © Copyright 1993 American Mathematical Society