We define the Milnor number of a one-dimensional holomorphic foliation $\mathcal{F}$ 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 $\mathcal{F}$ on a three-dimensional manifold with respect to $C$ is invariant by $C^1$ topological equivalences.

中文翻译：

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全纯叶面非孤立奇点的米尔诺数及其拓扑不变性

我们定义一维全纯叶理的米尔诺数$\mathcal{F}$作为两个全纯截面相对于紧连通分量的交集数$C$它的奇异集。在一定条件下，我们证明了 Milnor 数$\mathcal{F}$在三维流形上$C$不变的$C^{\mathrm{1个}}$拓扑等价。