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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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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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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).

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  • Automorphisms
  • Homotopy equivalence
  • Alexandroff spaces
  • Posets

Mathematics Subject Classification

  • 55P10
  • 55P99
  • 06A06