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On some topological realizations of groups and homomorphisms

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dc.contributor.authorChocano Feito, Pedro José
dc.contributor.authorAlonso Morón, Manuel
dc.contributor.authorRomero Ruiz Del Portal, Francisco
dc.date.accessioned2023-06-22T10:48:22Z
dc.date.available2023-06-22T10:48:22Z
dc.date.issued2022-08-24
dc.description.abstractGiven 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.en
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidades (España)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/73181
dc.identifier.citationChocano 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.
dc.identifier.doi10.1090/tran/8719
dc.identifier.issn0002-9947
dc.identifier.officialurlhttps://doi.org/10.1090/tran/8719
dc.identifier.relatedurlhttps://www.ams.org/journals/tran/2022-375-12/S0002-9947-2022-08719-5/S0002-9947-2022-08719-5.pdf
dc.identifier.urihttps://hdl.handle.net/20.500.14352/71700
dc.issue.number12
dc.journal.titleTransactions of the American Mathematical Society
dc.language.isoeng
dc.page.final8649
dc.page.initial8635
dc.publisherAmerican Mathematical Society
dc.relation.projectIDPGC2018-098321-B-100; BES-2016-076669
dc.rights.accessRightsopen access
dc.subject.cdu512.542.7
dc.subject.keywordAutomorphism group
dc.subject.keywordHomotopy equivalence
dc.subject.keywordAlexandroff spaces
dc.subject.keywordPosets
dc.subject.keywordHomology groups
dc.subject.keywordHomotopy groups
dc.subject.ucmGrupos (Matemáticas)
dc.subject.ucmTeoría de conjuntos
dc.subject.ucmTopología
dc.subject.unesco1201.02 Teoría Axiomática de Conjuntos
dc.subject.unesco1210 Topología
dc.titleOn some topological realizations of groups and homomorphismsen
dc.typejournal article
dc.volume.number375
dspace.entity.typePublication
relation.isAuthorOfPublicatione4503677-6189-4b18-be22-23d31611f2a4
relation.isAuthorOfPublication95bd8189-3086-4e0f-94f6-06dee8c8f675
relation.isAuthorOfPublication5c796e83-3a3a-466d-821f-de3280112781
relation.isAuthorOfPublication.latestForDiscoverye4503677-6189-4b18-be22-23d31611f2a4

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