Cohomological localizations and set-theoretical reflection
Homological localizations of spaces and spectra have been a fundamental tool in algebraic topology since the decade of 1970, especially in the setting of chromatic homotopy. However, it is unknown whether the existence of cohomological localizations can be proved in ZFC or not. Although this is appa...
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| Tipo de recurso: | capítulo de libro |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2023 |
| 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:2445/218296 |
| Acceso en línea: | https://hdl.handle.net/2445/218296 https://doi-org.sire.ub.edu/10.1007/978-3-031-12244-6_13 |
| Access Level: | acceso embargado |
| Palabra clave: | Teoria de l'homotopia Topologia algebraica Homotopy theory Algebraic topology |
| Sumario: | Homological localizations of spaces and spectra have been a fundamental tool in algebraic topology since the decade of 1970, especially in the setting of chromatic homotopy. However, it is unknown whether the existence of cohomological localizations can be proved in ZFC or not. Although this is apparently a homotopy-theoretical problem, it turned out to be closely related with set-theoretical reflection principles and therefore with the existence of large cardinals. In this note we present the state of the art with enough background so that proofs of results are readable by both topologists and set theorists. |
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