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Title: Localizing with respect to self-maps of the circle
Author: Casacuberta, Carles
Peschke, Georg
Keywords: Teoria de l'homotopia
Àlgebra homològica
Teoria de grups
Topologia algebraica
Homotopy theory
Homological algebra
Group theory
Algebraic topology
Issue Date: Sep-1993
Publisher: American Mathematical Society (AMS)
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.
Note: Reproducció del document publicat a:
It is part of: Transactions of the American Mathematical Society, 1993, vol. 339, num. 1, p. 117-140
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ISSN: 0002-9947
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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