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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On some topological realizations of groups and homomorphisms
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by Pedro J. Chocano, Manuel A. Morón and Francisco R. Ruiz del Portal PDF
Trans. Amer. Math. Soc. 375 (2022), 8635-8649 Request permission

Abstract:

Given a homomorphism of groups $f:G\rightarrow H$, we construct a topological space $X_f$ such that its group of homeomorphisms $Aut(X_f)$ is isomorphic to $G$, its group of homotopy classes of self-homotopy equivalences $\mathcal {E}(X_f)$ is isomorphic to $H$ and the natural map between $Aut(X_f)$ and $\mathcal {E}(X_f)$ is $f$. In addition, we consider realization problems involving homology groups, homotopy groups and groups of automorphisms.
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Additional Information
  • Pedro J. Chocano
  • Affiliation: Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, ESCET Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
  • MR Author ID: 1416097
  • ORCID: 0000-0003-0447-7212
  • Email: pedro.chocano@urjc.es
  • Manuel A. Morón
  • Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad Complutense de Madrid and Instituto de Matématica Interdisciplinar, Plaza de Ciencias 3, 28040 Madrid, Spain
  • ORCID: 0000-0003-1163-9291
  • Email: ma_moron@mat.ucm.es
  • Francisco R. Ruiz del Portal
  • Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad Complutense de Madrid and Instituto de Matématica Interdisciplinar, Plaza de Ciencias 3, 28040 Madrid, Spain
  • ORCID: 0000-0001-5476-0193
  • Email: R_Portal@mat.ucm.es
  • Received by editor(s): April 15, 2021
  • Received by editor(s) in revised form: November 15, 2021, and March 7, 2022
  • Published electronically: August 24, 2022
  • Additional Notes: This research was partially supported by Grants PGC2018-098321-B-100 and BES-2016-076669 from Ministerio de Ciencia, Innovación y Universidades (Spain).
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 8635-8649
  • MSC (2020): Primary 20B25, 06A06, 06A11, 05E18, 55P10, 55P99
  • DOI: https://doi.org/10.1090/tran/8719