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

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dc.contributor.authorBatista, Erica Boizan
dc.contributor.authorCosta, Joaõ Carlos Ferreira [UNESP]
dc.contributor.authorNunõ-Ballesteros, Juan J.
dc.contributor.institutionUniversidade Federal de Saõ Carlos
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversitat de València
dc.date.accessioned2018-12-11T17:07:36Z
dc.date.available2018-12-11T17:07:36Z
dc.date.issued2017-05-01
dc.description.abstractWe consider finitely determined map germs f : (ℝ3, 0) → (ℝ2, 0) with f -1(0) = {0} and we look at the classification of this kind of germ with respect to topological equivalence. By Fukuda's cone structure theorem, the topological type of f can be determined by the topological type of its associated link, which is a stable map from S 2 to S 1. We define a generalized version of the Reeb graph for stable maps γ : S 2 → S 1, which turns out to be a complete topological invariant. If f has corank 1, then f can be seen as a stabilization of a function h0: (ℝ2, 0) → (ℝ, 0), and we show that the Reeb graph is the sum of the partial trees of the positive and negative stabilizations of h 0. Finally, we apply this to give a complete topological description of all map germs with Boardman symbol Σ 2, 1.en
dc.description.affiliationDepartamento de Matemática Universidade Federal de Saõ Carlos, Caixa Postal 676
dc.description.affiliationDepartamento de Matemática IBILCE-UNESP Campus de Saõ José
dc.description.affiliationDepartament de Geometria i Topologia Universitat de València Campus de Burjassot
dc.description.affiliationUnespDepartamento de Matemática IBILCE-UNESP Campus de Saõ José
dc.format.extent319-348
dc.identifierhttp://dx.doi.org/10.1017/S0013091516000274
dc.identifier.citationProceedings of the Edinburgh Mathematical Society, v. 60, n. 2, p. 319-348, 2017.
dc.identifier.doi10.1017/S0013091516000274
dc.identifier.file2-s2.0-84994627208.pdf
dc.identifier.issn0013-0915
dc.identifier.scopus2-s2.0-84994627208
dc.identifier.urihttp://hdl.handle.net/11449/173756
dc.language.isoeng
dc.relation.ispartofProceedings of the Edinburgh Mathematical Society
dc.relation.ispartofsjr0,695
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 Isolated Zerosen
dc.typeArtigo

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