{"title":"全纯叶的非孤立奇点Milnor数及其拓扑不变性","authors":"Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas Bazán","doi":"10.1112/topo.12281","DOIUrl":null,"url":null,"abstract":"<p>We define the Milnor number of a one-dimensional holomorphic foliation <math>\n <semantics>\n <mi>F</mi>\n <annotation>$\\mathcal {F}$</annotation>\n </semantics></math> as the intersection number of two holomorphic sections with respect to a compact connected component <math>\n <semantics>\n <mi>C</mi>\n <annotation>$C$</annotation>\n </semantics></math> of its singular set. Under certain conditions, we prove that the Milnor number of <math>\n <semantics>\n <mi>F</mi>\n <annotation>$\\mathcal {F}$</annotation>\n </semantics></math> on a three-dimensional manifold with respect to <math>\n <semantics>\n <mi>C</mi>\n <annotation>$C$</annotation>\n </semantics></math> is invariant by <math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mn>1</mn>\n </msup>\n <annotation>$C^1$</annotation>\n </semantics></math> topological equivalences.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance\",\"authors\":\"Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas Bazán\",\"doi\":\"10.1112/topo.12281\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We define the Milnor number of a one-dimensional holomorphic foliation <math>\\n <semantics>\\n <mi>F</mi>\\n <annotation>$\\\\mathcal {F}$</annotation>\\n </semantics></math> as the intersection number of two holomorphic sections with respect to a compact connected component <math>\\n <semantics>\\n <mi>C</mi>\\n <annotation>$C$</annotation>\\n </semantics></math> of its singular set. Under certain conditions, we prove that the Milnor number of <math>\\n <semantics>\\n <mi>F</mi>\\n <annotation>$\\\\mathcal {F}$</annotation>\\n </semantics></math> on a three-dimensional manifold with respect to <math>\\n <semantics>\\n <mi>C</mi>\\n <annotation>$C$</annotation>\\n </semantics></math> is invariant by <math>\\n <semantics>\\n <msup>\\n <mi>C</mi>\\n <mn>1</mn>\\n </msup>\\n <annotation>$C^1$</annotation>\\n </semantics></math> topological equivalences.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12281\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12281","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance
We define the Milnor number of a one-dimensional holomorphic foliation as the intersection number of two holomorphic sections with respect to a compact connected component of its singular set. Under certain conditions, we prove that the Milnor number of on a three-dimensional manifold with respect to is invariant by topological equivalences.
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