The Reeb Graph of a Map Germ from R3 to R2 with Non Isolated Zeros

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dc.contributor.authorBatista, Erica Boizan
dc.contributor.authorCosta, João Carlos Ferreira [UNESP]
dc.contributor.authorNuño-Ballesteros, Juan J.
dc.contributor.institutionUniversidade Federal do Cariri
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversitat de València
dc.date.accessioned2018-12-11T17:16:03Z
dc.date.available2018-12-11T17:16:03Z
dc.date.issued2018-06-01
dc.description.abstractWe consider the topological classification of finitely determined map germs [f] : (R3, 0) → (R2, 0) with f- 1(0) ≠ { 0 }. The case f- 1(0) = { 0 } was treated in another recent paper by the authors. The main tool used to describe the topological type is the link of [f], which is obtained by taking the intersection of its image with a small sphere Sδ1 centered at the origin. The link is a stable map γf: N→ S1, where N is diffeomorphic to a sphere S2 minus 2L disks. We define a complete topological invariant called the generalized Reeb graph. Finally, we apply our results to give a topological description of some map germs with Boardman symbol Σ 2 , 1.en
dc.description.affiliationCentro de Ciências e Tecnologia Universidade Federal do Cariri
dc.description.affiliationDepartamento de Matemática IBILCE-UNESP, Campus de São José do Rio Preto
dc.description.affiliationDepartament de Matemàtiques Universitat de València, Campus de Burjassot
dc.description.affiliationUnespDepartamento de Matemática IBILCE-UNESP, Campus de São José do Rio Preto
dc.format.extent369-394
dc.identifierhttp://dx.doi.org/10.1007/s00574-017-0058-4
dc.identifier.citationBulletin of the Brazilian Mathematical Society, v. 49, n. 2, p. 369-394, 2018.
dc.identifier.doi10.1007/s00574-017-0058-4
dc.identifier.file2-s2.0-85034217440.pdf
dc.identifier.issn1678-7544
dc.identifier.scopus2-s2.0-85034217440
dc.identifier.urihttp://hdl.handle.net/11449/175496
dc.language.isoeng
dc.relation.ispartofBulletin of the Brazilian Mathematical Society
dc.relation.ispartofsjr0,406
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectClassification
dc.subjectLink
dc.subjectReeb graph
dc.subjectTopological equivalence
dc.titleThe Reeb Graph of a Map Germ from R3 to R2 with Non Isolated Zerosen
dc.typeArtigo
unesp.author.orcid0000-0002-0428-4640[2]

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