Z2-bordism and the Borsuk–Ulam Theorem
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s00229-015-0809-8 http://hdl.handle.net/11449/172280 |
Resumo: | The purpose of this work is to classify, for given integers m,n≥1, the bordism class of a closed smooth m-manifold Xm with a free smooth involution τ with respect to the validity of the Borsuk–Ulam property that for every continuous map φ: Xm→ Rn there exists a point x∈ Xm such that φ(x) = φ(τ(x)). We will classify a given free Z2-bordism class α according to the three possible cases that (a) all representatives (Xm, τ) of α satisfy the Borsuk–Ulam property; (b) there are representatives (X1m,τ1) and (X2m,τ2) of α such that (X1m,τ1) satisfies the Borsuk–Ulam property but (X2m,τ2) does not; (c) no representative (Xm, τ) of α satisfies the Borsuk–Ulam property. |
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Repositório Institucional da UNESP |
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Z2-bordism and the Borsuk–Ulam Theorem55M3557R75Primary 55M20Secondary 57R85The purpose of this work is to classify, for given integers m,n≥1, the bordism class of a closed smooth m-manifold Xm with a free smooth involution τ with respect to the validity of the Borsuk–Ulam property that for every continuous map φ: Xm→ Rn there exists a point x∈ Xm such that φ(x) = φ(τ(x)). We will classify a given free Z2-bordism class α according to the three possible cases that (a) all representatives (Xm, τ) of α satisfy the Borsuk–Ulam property; (b) there are representatives (X1m,τ1) and (X2m,τ2) of α such that (X1m,τ1) satisfies the Borsuk–Ulam property but (X2m,τ2) does not; (c) no representative (Xm, τ) of α satisfies the Borsuk–Ulam property.Department of Mathematics University of AberdeenDepartamento de Matemática IME - Universidade de São Paulo, Ag. Cidade de São Paulo, Caixa Postal 66281Departamento de Matemática IGCE - UNESPDepartamento de Matemática Universidade Federal de São Carlos, Caixa Postal 676Departamento de Matemática IGCE - UNESPUniversity of AberdeenUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Universidade Federal de São Carlos (UFSCar)Crabb, M. C.Gonçalves, D. L.Libardi, A. K.M. [UNESP]Pergher, P. L.Q.2018-12-11T16:59:30Z2018-12-11T16:59:30Z2016-07-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article371-381application/pdfhttp://dx.doi.org/10.1007/s00229-015-0809-8Manuscripta Mathematica, v. 150, n. 3-4, p. 371-381, 2016.0025-2611http://hdl.handle.net/11449/17228010.1007/s00229-015-0809-82-s2.0-849495053822-s2.0-84949505382.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengManuscripta Mathematica1,053info:eu-repo/semantics/openAccess2023-10-30T06:12:03Zoai:repositorio.unesp.br:11449/172280Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:28:31.829100Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Z2-bordism and the Borsuk–Ulam Theorem |
title |
Z2-bordism and the Borsuk–Ulam Theorem |
spellingShingle |
Z2-bordism and the Borsuk–Ulam Theorem Crabb, M. C. 55M35 57R75 Primary 55M20 Secondary 57R85 |
title_short |
Z2-bordism and the Borsuk–Ulam Theorem |
title_full |
Z2-bordism and the Borsuk–Ulam Theorem |
title_fullStr |
Z2-bordism and the Borsuk–Ulam Theorem |
title_full_unstemmed |
Z2-bordism and the Borsuk–Ulam Theorem |
title_sort |
Z2-bordism and the Borsuk–Ulam Theorem |
author |
Crabb, M. C. |
author_facet |
Crabb, M. C. Gonçalves, D. L. Libardi, A. K.M. [UNESP] Pergher, P. L.Q. |
author_role |
author |
author2 |
Gonçalves, D. L. Libardi, A. K.M. [UNESP] Pergher, P. L.Q. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
University of Aberdeen Universidade de São Paulo (USP) Universidade Estadual Paulista (Unesp) Universidade Federal de São Carlos (UFSCar) |
dc.contributor.author.fl_str_mv |
Crabb, M. C. Gonçalves, D. L. Libardi, A. K.M. [UNESP] Pergher, P. L.Q. |
dc.subject.por.fl_str_mv |
55M35 57R75 Primary 55M20 Secondary 57R85 |
topic |
55M35 57R75 Primary 55M20 Secondary 57R85 |
description |
The purpose of this work is to classify, for given integers m,n≥1, the bordism class of a closed smooth m-manifold Xm with a free smooth involution τ with respect to the validity of the Borsuk–Ulam property that for every continuous map φ: Xm→ Rn there exists a point x∈ Xm such that φ(x) = φ(τ(x)). We will classify a given free Z2-bordism class α according to the three possible cases that (a) all representatives (Xm, τ) of α satisfy the Borsuk–Ulam property; (b) there are representatives (X1m,τ1) and (X2m,τ2) of α such that (X1m,τ1) satisfies the Borsuk–Ulam property but (X2m,τ2) does not; (c) no representative (Xm, τ) of α satisfies the Borsuk–Ulam property. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-07-01 2018-12-11T16:59:30Z 2018-12-11T16:59:30Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s00229-015-0809-8 Manuscripta Mathematica, v. 150, n. 3-4, p. 371-381, 2016. 0025-2611 http://hdl.handle.net/11449/172280 10.1007/s00229-015-0809-8 2-s2.0-84949505382 2-s2.0-84949505382.pdf |
url |
http://dx.doi.org/10.1007/s00229-015-0809-8 http://hdl.handle.net/11449/172280 |
identifier_str_mv |
Manuscripta Mathematica, v. 150, n. 3-4, p. 371-381, 2016. 0025-2611 10.1007/s00229-015-0809-8 2-s2.0-84949505382 2-s2.0-84949505382.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Manuscripta Mathematica 1,053 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
371-381 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128657759141888 |