Coincidence of pairs of maps on torus fibre bundles over the circle
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s11784-020-0761-4 http://hdl.handle.net/11449/201115 |
Resumo: | Let f, g: M(ϕ1) → M(ϕ2) be fibre-preserving maps over the circle, S1, where M(ϕ1) and M(ϕ2) are fibre bundles over S1 and the fibre is the torus, T. The main purpose of this work is to classify the pairs of maps (f, g) which can be deformed by fibrewise homotopy over S1 to a coincidence-free pair (f′, g′) , f′, g′: M(ϕ1) → M(ϕ2). In general, the classification of such pairs of maps is equivalent to finding solutions for an equation in the free group π2(T, T- 1) , called the main equation. In certain situations, it is appropriate to study the main equation in the abelianization of π2(T, T- 1) or on some quotients of this group, since, if the equation in one of these quotients does not admit solution, then the original equation also does not admit solution. In this case, it is not possible to obtain the desired deformability. |
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Coincidence of pairs of maps on torus fibre bundles over the circleCoincidencefibre-preserving mapsT-fibre bundlesLet f, g: M(ϕ1) → M(ϕ2) be fibre-preserving maps over the circle, S1, where M(ϕ1) and M(ϕ2) are fibre bundles over S1 and the fibre is the torus, T. The main purpose of this work is to classify the pairs of maps (f, g) which can be deformed by fibrewise homotopy over S1 to a coincidence-free pair (f′, g′) , f′, g′: M(ϕ1) → M(ϕ2). In general, the classification of such pairs of maps is equivalent to finding solutions for an equation in the free group π2(T, T- 1) , called the main equation. In certain situations, it is appropriate to study the main equation in the abelianization of π2(T, T- 1) or on some quotients of this group, since, if the equation in one of these quotients does not admit solution, then the original equation also does not admit solution. In this case, it is not possible to obtain the desired deformability.Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista (UNESP)Campus Avançado Tupã Instituto Federal de Educação Ciência e Tecnologia de São Paulo (IFSP)Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista (UNESP)Universidade Estadual Paulista (Unesp)Instituto Federal de Educação Ciência e Tecnologia de São Paulo (IFSP)Vieira, J. P. [UNESP]Silva, L. S.2020-12-12T02:24:28Z2020-12-12T02:24:28Z2020-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s11784-020-0761-4Journal of Fixed Point Theory and Applications, v. 22, n. 2, 2020.1661-77461661-7738http://hdl.handle.net/11449/20111510.1007/s11784-020-0761-42-s2.0-85082041521Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Fixed Point Theory and Applicationsinfo:eu-repo/semantics/openAccess2024-06-10T14:49:17Zoai:repositorio.unesp.br:11449/201115Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:19:35.692198Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Coincidence of pairs of maps on torus fibre bundles over the circle |
title |
Coincidence of pairs of maps on torus fibre bundles over the circle |
spellingShingle |
Coincidence of pairs of maps on torus fibre bundles over the circle Vieira, J. P. [UNESP] Coincidence fibre-preserving maps T-fibre bundles |
title_short |
Coincidence of pairs of maps on torus fibre bundles over the circle |
title_full |
Coincidence of pairs of maps on torus fibre bundles over the circle |
title_fullStr |
Coincidence of pairs of maps on torus fibre bundles over the circle |
title_full_unstemmed |
Coincidence of pairs of maps on torus fibre bundles over the circle |
title_sort |
Coincidence of pairs of maps on torus fibre bundles over the circle |
author |
Vieira, J. P. [UNESP] |
author_facet |
Vieira, J. P. [UNESP] Silva, L. S. |
author_role |
author |
author2 |
Silva, L. S. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Instituto Federal de Educação Ciência e Tecnologia de São Paulo (IFSP) |
dc.contributor.author.fl_str_mv |
Vieira, J. P. [UNESP] Silva, L. S. |
dc.subject.por.fl_str_mv |
Coincidence fibre-preserving maps T-fibre bundles |
topic |
Coincidence fibre-preserving maps T-fibre bundles |
description |
Let f, g: M(ϕ1) → M(ϕ2) be fibre-preserving maps over the circle, S1, where M(ϕ1) and M(ϕ2) are fibre bundles over S1 and the fibre is the torus, T. The main purpose of this work is to classify the pairs of maps (f, g) which can be deformed by fibrewise homotopy over S1 to a coincidence-free pair (f′, g′) , f′, g′: M(ϕ1) → M(ϕ2). In general, the classification of such pairs of maps is equivalent to finding solutions for an equation in the free group π2(T, T- 1) , called the main equation. In certain situations, it is appropriate to study the main equation in the abelianization of π2(T, T- 1) or on some quotients of this group, since, if the equation in one of these quotients does not admit solution, then the original equation also does not admit solution. In this case, it is not possible to obtain the desired deformability. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T02:24:28Z 2020-12-12T02:24:28Z 2020-06-01 |
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/10.1007/s11784-020-0761-4 Journal of Fixed Point Theory and Applications, v. 22, n. 2, 2020. 1661-7746 1661-7738 http://hdl.handle.net/11449/201115 10.1007/s11784-020-0761-4 2-s2.0-85082041521 |
url |
http://dx.doi.org/10.1007/s11784-020-0761-4 http://hdl.handle.net/11449/201115 |
identifier_str_mv |
Journal of Fixed Point Theory and Applications, v. 22, n. 2, 2020. 1661-7746 1661-7738 10.1007/s11784-020-0761-4 2-s2.0-85082041521 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Fixed Point Theory and Applications |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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_ |
1808129052283764736 |