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

Autor:	Arturo Fernández‐Pérez, Gilcione Nonato Costa, Rudy Rosas Bazán
Rok vydání:	2021
Předmět:	Mathematics - Geometric Topology Mathematics - Complex Variables FOS: Mathematics 32S65 - 58K45 Geometric Topology (math.GT) Geometry and Topology Complex Variables (math.CV) Mathematics::Geometric Topology Mathematics::Symplectic Geometry
DOI:	10.48550/arxiv.2109.00053
Popis:	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. Comment: 17 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e3a33df16f130c5a0f103bbc80d06db Zobrazit plný text záznamu