Topological realizations of groups in Alexandroff spaces
Given a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version are isomorphic to G. As a result, any group G can be r...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7571 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/7571 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.56 512.541.5 515.143 Automorphisms Homotopy equivalence Alexandroff spaces Posets Álgebra Grupos (Matemáticas) Topología 1201 Álgebra 1210 Topología |
| Resumo: | Given a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version are isomorphic to G. As a result, any group G can be realized as the group of homotopy classes of self-homotopy equivalences of a topological space X, for which there exists a CW complex K(X) and a weak homotopy equivalence from K(X) to X. |
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