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Topological realizations of groups in Alexandroff spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

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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Acknowledgements

We would like to thank the referee for carefully reading our manuscript and for giving such valuable comments which substantially improved some previous versions of the paper.

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Authors and Affiliations

  1. Departamento de Álgebra, Geometría y Topología, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040, Madrid, Spain

    Pedro J. Chocano

  2. Departamento de Álgebra, Geometría y Topología, Instituto de Matematica Interdisciplinar, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040, Madrid, Spain

    Manuel A. Morón & Francisco Ruiz del Portal

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  1. Pedro J. Chocano
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  2. Manuel A. Morón
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  3. Francisco Ruiz del Portal
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Correspondence to Pedro J. Chocano.

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This research is partially supported by Grants MTM2015-63612-P, PGC2018-098321-B-100 and BES-2016-076669 from Ministerio de Ciencia, Innovación y Universidades (Spain).

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Chocano, P.J., Morón, M.A. & Ruiz del Portal, F. Topological realizations of groups in Alexandroff spaces. RACSAM 115, 25 (2021). https://doi.org/10.1007/s13398-020-00964-7

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