On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2023-02-06 DOI:10.1112/topo.12281

Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas Bazán

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Abstract

We define the Milnor number of a one-dimensional holomorphic foliation $F$ as the intersection number of two holomorphic sections with respect to a compact connected component $C$ of its singular set. Under certain conditions, we prove that the Milnor number of $F$ on a three-dimensional manifold with respect to $C$ is invariant by $C^{1}$ topological equivalences.

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全纯叶的非孤立奇点Milnor数及其拓扑不变性

我们将一维全纯叶理F$\mathcal｛F｝$的Milnor数定义为两个全纯截面相对于其奇异集的紧连通分量C$C$的交集数。在一定条件下，我们证明了三维流形上F$\mathcal｛F｝$相对于C$C$的Milnor数通过C1$C^1$拓扑等价是不变的。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.