Closed model categories for [n,m]-types
For m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m∼. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both struct...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1997 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc6a15b750603269e826b7 |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc6a15b750603269e826b7 |
| Access Level: | acceso abierto |
| Palabra clave: | [n m]-types Closed model category Homotopy category |
| Sumario: | For m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m∼. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both structures have the same class of weak equivalences but different classes of fibrations and therefore of cofibrations. Using one of these structures, one obtains that the localized category is equivalent to the category of n-reduced CW-complexes with dimension less than or equal to m+1 and m-homotopy classes of cellular pointed maps. Using the other structure we see that the localized category is also equivalent to the homotopy category of (n-1)-connected (m+1)-coconnected CW-complexes. |
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