On some topological realizations of groups and homomorphisms

Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, Francisco

On some topological realizations of groups and homomorphisms

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Official URL

https://doi.org/10.1090/tran/8719

Publication date

2022

Authors

Chocano Feito, Pedro José

Alonso Morón, Manuel

Romero Ruiz Del Portal, Francisco

Publisher

American Mathematical Society

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URI

https://hdl.handle.net/20.500.14352/71700

Citation

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.