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...
| Autores: | , |
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| 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 |
| 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. |
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