Involutions fixing F-n U F-3
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.indag.2018.01.003 http://hdl.handle.net/11449/164082 |
Resumo: | Let Mm be a closed smooth manifold equipped with a smooth involution having fixed point set of the form F-n U F-3, where F-n and F-3 are submanifolds with dimensions n and 3, respectively, where 3 < n < m and with the normal bundles over F-n and F-3 being nonbounding. The authors of this paper, together with Patricia E. Desideri, previously showed that, when n is even, then m <= n + 4, which we call a small codimension phenomenon.-Further, they showed that this small bound is.best posiible. In this paper we study this problem for n odd, which is much more complicated, requiring more sophisticated techniques involving characteristic numbers. We show in this case that'm <= M(n - 3) + 6, where M(n) is the Stong Pergher number (see the definition of M(n) in Section 1). Further, we show that this bound is almost best possible, in the sense that there exists an example with m = M(n - 3) + 5, which means that for n odd the small codimension phenomenon does not occur and the bound in question is meaningful. The existence of these bounds is guaranteed by the famous Five Halves Theorem of J. Boardman, which establishes that, under the above hypotheses, m <= 5/2 n. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved. |
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Involutions fixing F-n U F-3InvolutionFixed-dataWhitney numberWu formulaSteenrod operationStong-Pergher numberLet Mm be a closed smooth manifold equipped with a smooth involution having fixed point set of the form F-n U F-3, where F-n and F-3 are submanifolds with dimensions n and 3, respectively, where 3 < n < m and with the normal bundles over F-n and F-3 being nonbounding. The authors of this paper, together with Patricia E. Desideri, previously showed that, when n is even, then m <= n + 4, which we call a small codimension phenomenon.-Further, they showed that this small bound is.best posiible. In this paper we study this problem for n odd, which is much more complicated, requiring more sophisticated techniques involving characteristic numbers. We show in this case that'm <= M(n - 3) + 6, where M(n) is the Stong Pergher number (see the definition of M(n) in Section 1). Further, we show that this bound is almost best possible, in the sense that there exists an example with m = M(n - 3) + 5, which means that for n odd the small codimension phenomenon does not occur and the bound in question is meaningful. The existence of these bounds is guaranteed by the famous Five Halves Theorem of J. Boardman, which establishes that, under the above hypotheses, m <= 5/2 n. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Univ Estadual Paulista Ibilce, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13565905 Sao Carlos, SP, BrazilUniv Estadual Paulista Ibilce, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilElsevier B.V.Universidade Estadual Paulista (Unesp)Universidade Federal de São Carlos (UFSCar)Barbaresco, Evelin M. [UNESP]Pergher, Pedro L. Q.2018-11-26T17:49:03Z2018-11-26T17:49:03Z2018-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article807-818application/pdfhttp://dx.doi.org/10.1016/j.indag.2018.01.003Indagationes Mathematicae-new Series. Amsterdam: Elsevier Science Bv, v. 29, n. 2, p. 807-818, 2018.0019-3577http://hdl.handle.net/11449/16408210.1016/j.indag.2018.01.003WOS:000429511400019WOS000429511400019.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIndagationes Mathematicae-new Series0,685info:eu-repo/semantics/openAccess2023-11-24T06:15:48Zoai:repositorio.unesp.br:11449/164082Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:36:12.425063Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Involutions fixing F-n U F-3 |
title |
Involutions fixing F-n U F-3 |
spellingShingle |
Involutions fixing F-n U F-3 Barbaresco, Evelin M. [UNESP] Involution Fixed-data Whitney number Wu formula Steenrod operation Stong-Pergher number |
title_short |
Involutions fixing F-n U F-3 |
title_full |
Involutions fixing F-n U F-3 |
title_fullStr |
Involutions fixing F-n U F-3 |
title_full_unstemmed |
Involutions fixing F-n U F-3 |
title_sort |
Involutions fixing F-n U F-3 |
author |
Barbaresco, Evelin M. [UNESP] |
author_facet |
Barbaresco, Evelin M. [UNESP] Pergher, Pedro L. Q. |
author_role |
author |
author2 |
Pergher, Pedro L. Q. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Federal de São Carlos (UFSCar) |
dc.contributor.author.fl_str_mv |
Barbaresco, Evelin M. [UNESP] Pergher, Pedro L. Q. |
dc.subject.por.fl_str_mv |
Involution Fixed-data Whitney number Wu formula Steenrod operation Stong-Pergher number |
topic |
Involution Fixed-data Whitney number Wu formula Steenrod operation Stong-Pergher number |
description |
Let Mm be a closed smooth manifold equipped with a smooth involution having fixed point set of the form F-n U F-3, where F-n and F-3 are submanifolds with dimensions n and 3, respectively, where 3 < n < m and with the normal bundles over F-n and F-3 being nonbounding. The authors of this paper, together with Patricia E. Desideri, previously showed that, when n is even, then m <= n + 4, which we call a small codimension phenomenon.-Further, they showed that this small bound is.best posiible. In this paper we study this problem for n odd, which is much more complicated, requiring more sophisticated techniques involving characteristic numbers. We show in this case that'm <= M(n - 3) + 6, where M(n) is the Stong Pergher number (see the definition of M(n) in Section 1). Further, we show that this bound is almost best possible, in the sense that there exists an example with m = M(n - 3) + 5, which means that for n odd the small codimension phenomenon does not occur and the bound in question is meaningful. The existence of these bounds is guaranteed by the famous Five Halves Theorem of J. Boardman, which establishes that, under the above hypotheses, m <= 5/2 n. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-11-26T17:49:03Z 2018-11-26T17:49:03Z 2018-04-01 |
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/10.1016/j.indag.2018.01.003 Indagationes Mathematicae-new Series. Amsterdam: Elsevier Science Bv, v. 29, n. 2, p. 807-818, 2018. 0019-3577 http://hdl.handle.net/11449/164082 10.1016/j.indag.2018.01.003 WOS:000429511400019 WOS000429511400019.pdf |
url |
http://dx.doi.org/10.1016/j.indag.2018.01.003 http://hdl.handle.net/11449/164082 |
identifier_str_mv |
Indagationes Mathematicae-new Series. Amsterdam: Elsevier Science Bv, v. 29, n. 2, p. 807-818, 2018. 0019-3577 10.1016/j.indag.2018.01.003 WOS:000429511400019 WOS000429511400019.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Indagationes Mathematicae-new Series 0,685 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
807-818 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science 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_ |
1808128955382759424 |