On some topological realizations of groups and homomorphisms
Given a homomorphism of groups f : G → H, we construct a topological space Xf such that its group of homeomorphisms Aut(Xf) is isomorphic to G, its group of homotopy classes of self-homotopy equivalences E(Xf) is isomorphic to H and the natural map between Aut(Xf) and E(Xf) is f. In addition, we con...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71700 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71700 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.542.7 Automorphism group Homotopy equivalence Alexandroff spaces Posets Homology groups Homotopy groups Grupos (Matemáticas) Teoría de conjuntos Topología 1201.02 Teoría Axiomática de Conjuntos 1210 Topología |
| Sumario: | Given a homomorphism of groups f : G → H, we construct a topological space Xf such that its group of homeomorphisms Aut(Xf) is isomorphic to G, its group of homotopy classes of self-homotopy equivalences E(Xf) is isomorphic to H and the natural map between Aut(Xf) and E(Xf) is f. In addition, we consider realization problems involving homology groups, homotopy groups and groups of automorphisms. |
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