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Topological realizations of groups in Alexandroff spaces

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Chocano Feito, Pedro José and Morón, Manuel A. and Romero Ruiz del Portal, Francisco (2020) Topological realizations of groups in Alexandroff spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115 (1). ISSN 1578-7303

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Official URL: https://doi.org/10.1007/s13398-020-00964-7




Abstract

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.


Item Type:Article
Additional Information:

This is a pre-print of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas . The final authenticated version is available online at: https://doi.org/10.1007/s13398-020-00964-7”.

Uncontrolled Keywords:Automorphisms; Homotopy equivalence; Alexandroff spaces; Posets
Subjects:Sciences > Mathematics > Algebra
Sciences > Mathematics > Group Theory
Sciences > Mathematics > Topology
ID Code:63263
Deposited On:02 Dec 2020 14:55
Last Modified:02 Dec 2020 15:30

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