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1993-09

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/96481

Localizing with respect to self-maps of the circle

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Related resource

http://dx.doi.org/10.1090/S0002-9947-1993-1123451-X

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.

Subject

Teoria de l'homotopia, Àlgebra homològica, Teoria de grups, Topologia algebraica

Subject (English)

Homotopy theory, Homological algebra, Group theory, Algebraic topology

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CASACUBERTA, Carles and PESCHKE, Georg. Localizing with respect to self-maps of the circle. Transactions of the American Mathematical Society. 1993. Vol. 339, num. 1, pags. 117-140. ISSN 0002-9947. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/96481

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