Chocano Feito, Pedro JoséAlonso Morón, ManuelRomero Ruiz Del Portal, Francisco2023-06-222023-06-222022-08-24Chocano Feito, P. J., Alonso Morón, M., Romero Ruiz Del Portal, F. «On Some Topological Realizations of Groups and Homomorphisms». Transactions of the American Mathematical Society, vol. 375, n.o 12, agosto de 2022, pp. 8635-49. DOI.org (Crossref), https://doi.org/10.1090/tran/8719.0002-994710.1090/tran/8719https://hdl.handle.net/20.500.14352/71700Given a homomorphism of groups f : G → H, we construct a topological space Xf such that its group of homeomorphisms Aut(Xf) is isomorphic to G, its group of homotopy classes of self-homotopy equivalences E(Xf) is isomorphic to H and the natural map between Aut(Xf) and E(Xf) is f. In addition, we consider realization problems involving homology groups, homotopy groups and groups of automorphisms.engjournal articlehttps://doi.org/10.1090/tran/8719https://www.ams.org/journals/tran/2022-375-12/S0002-9947-2022-08719-5/S0002-9947-2022-08719-5.pdfopen access512.542.7Automorphism groupHomotopy equivalenceAlexandroff spacesPosetsHomology groupsHomotopy groupsGrupos (Matemáticas)Teoría de conjuntosTopología1201.02 Teoría Axiomática de Conjuntos1210 Topología