Localizing with respect to self-maps of the circle

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{C...

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Detalles Bibliográficos
Autores: Casacuberta, Carles, Peschke, Georg
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1993
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/96481
Acceso en línea:https://hdl.handle.net/2445/96481
Access Level:acceso abierto
Palabra clave:Teoria de l'homotopia
Àlgebra homològica
Teoria de grups
Topologia algebraica
Homotopy theory
Homological algebra
Group theory
Algebraic topology
Descripción
Sumario: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.