Topological realizations of groups in Alexandroff spaces

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dc.contributor.authorChocano Feito, Pedro José
dc.contributor.authorAlonso Morón, Manuel
dc.contributor.authorRomero Ruiz Del Portal, Francisco
dc.date.accessioned2023-06-17T08:56:07Z
dc.date.available2023-06-17T08:56:07Z
dc.date.issued2020-11-23
dc.descriptionThis is a pre-print of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas . The final authenticated version is available online at: https://doi.org/10.1007/s13398-020-00964-7”.en
dc.description.abstractGiven a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version are isomorphic to G. As a result, any group G can be realized as the group of homotopy classes of self-homotopy equivalences of a topological space X, for which there exists a CW complex K(X) and a weak homotopy equivalence from K(X) to X.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 Economía, Comercio y Empresa (España)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/63263
dc.identifier.citationChocano Feito, P. J., Alonso Morón, M. y Romero Ruiz Del Portal, F. «Topological Realizations of Groups in Alexandroff Spaces». Revista de La Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 115, n.o 1, enero de 2021, p. 25. DOI.org (Crossref), https://doi.org/10.1007/s13398-020-00964-7.
dc.identifier.doi10.1007/s13398-020-00964-7
dc.identifier.issn1578-7303
dc.identifier.officialurlhttps://doi.org/10.1007/s13398-020-00964-7
dc.identifier.relatedurlhttps://link.springer.com/article/10.1007/s13398-020-00964-7
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7571
dc.issue.number1
dc.journal.titleRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
dc.language.isoeng
dc.publisherSpringer
dc.relation.projectID(MTM2015-63612-P; PGC2018-098321-B-100; BES-2016-076669)
dc.rights.accessRightsopen access
dc.subject.cdu512.56
dc.subject.cdu512.541.5
dc.subject.cdu515.143
dc.subject.keywordAutomorphisms
dc.subject.keywordHomotopy equivalence
dc.subject.keywordAlexandroff spaces
dc.subject.keywordPosets
dc.subject.ucmÁlgebra
dc.subject.ucmGrupos (Matemáticas)
dc.subject.ucmTopología
dc.subject.unesco1201 Álgebra
dc.subject.unesco1210 Topología
dc.titleTopological realizations of groups in Alexandroff spacesen
dc.typejournal article
dc.volume.number115
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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