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

@inproceedings{FernandezPerez2021OnTM, title={On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance}, author={Arturo Fern'andez-P'erez and Gilcione Nonato Costa and Rudy Rosas}, year={2021} }

We define the Milnor number – as the intersection number of two holomorphic sections – of a one-dimensional holomorphic foliation F 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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