On some topological realizations of groups and homomorphisms
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2022
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American Mathematical Society
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Chocano 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.
Abstract
Given 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.