Topological realizations of groups in Alexandroff spaces

We prove that every group can be realized as the homeomorphism group and as the group of (pointed) homotopy classes of (pointed) self-homotopy equivalences of infinitely many non-homotopy-equivalent Alexandroff spaces.

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Bibliographische Detailangaben
Veröffentlicht in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2021, Vol.115 (1), Article 25
Hauptverfasser:	Chocano, Pedro J., Morón, Manuel A., Ruiz del Portal, Francisco
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Equivalence Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical Topology
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Beschreibung
Zusammenfassung:	We prove that every group can be realized as the homeomorphism group and as the group of (pointed) homotopy classes of (pointed) self-homotopy equivalences of infinitely many non-homotopy-equivalent Alexandroff spaces.
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-020-00964-7