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arXiv · 2109.00053

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

Arturo Fernández-Pérez·Gilcione Nonato Costa·Rudy Rosas
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Abstract

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

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Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas. 2021-12-06. On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance. https://doi.org/10.1112/topo.12281

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