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http://hdl.handle.net/2445/184945
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DC Field | Value | Language |
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dc.contributor.author | Casacuberta, Carles | - |
dc.contributor.author | Rodríguez, José L. | - |
dc.contributor.author | Tai, Jin-yen | - |
dc.date.accessioned | 2022-04-13T08:17:00Z | - |
dc.date.available | 2022-04-13T08:17:00Z | - |
dc.date.issued | 2016-09-12 | - |
dc.identifier.issn | 1472-2747 | - |
dc.identifier.uri | http://hdl.handle.net/2445/184945 | - |
dc.description.abstract | We prove that every homotopical localization of the circle $S^{1}$ is an aspherical space whose fundamental group $A$ is abelian and admits a ring structure with unit such that the evaluation map End $(A) \rightarrow A$ at the unit is an isomorphism of rings. Since it is known that there is a proper class of nonisomorphic rings with this property, and we show that all occur in this way, it follows that there is a proper class of distinct homotopical localizations of spaces (in spite of the fact that homological localizations form a set). This answers a question asked by Farjoun in the nineties. More generally, we study localizations $L_{f} K(G, n)$ of Eilenberg-Mac Lane spaces with respect to any map $f$, where $n \geq 1$ and $G$ is any abelian group, and we show that many properties of $G$ are transferred to the homotopy groups of $L_{f} K(G, n)$. Among other results, we show that, if $X$ is a product of abelian Eilenberg-Mac Lane spaces and $f$ is any map, then the homotopy groups $\pi_{m}\left(L_{f} X\right)$ are modules over the ring $\pi_{1}\left(L_{f} S^{1}\right)$ in a canonical way. This explains and generalizes earlier observations made by other authors in the case of homological localizations. | - |
dc.format.extent | 42 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Mathematical Sciences Publishers (MSP) | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.2140/agt.2016.16.2379 | - |
dc.relation.ispartof | Algebraic and Geometric Topology, 2016, vol. 16, num. 4, p. 2379-2420 | - |
dc.relation.uri | https://doi.org/10.2140/agt.2016.16.2379 | - |
dc.rights | (c) Mathematical Sciences Publishers (MSP), 2016 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Teoria de l'homotopia | - |
dc.subject.classification | Anells associatius | - |
dc.subject.classification | Teoria de functors | - |
dc.subject.other | Homotopy theory | - |
dc.subject.other | Associative rings | - |
dc.subject.other | Functor theory | - |
dc.title | Localizations of abelian Eilenberg-Mac Lane spaces of finite type | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 669744 | - |
dc.date.updated | 2022-04-13T08:17:00Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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669744.pdf | 503.27 kB | Adobe PDF | View/Open |
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