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

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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