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

Arturo Fernández-Pérez; Gilcione Nonato Costa; Rudy Rosas

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

Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas

Sección de Matemáticas

Research output: Contribution to journal › Article › peer-review

Abstract

We define the Milnor number of a one-dimensional holomorphic foliation (Formula presented.) as the intersection number of two holomorphic sections with respect to a compact connected component (Formula presented.) of its singular set. Under certain conditions, we prove that the Milnor number of (Formula presented.) on a three-dimensional manifold with respect to (Formula presented.) is invariant by (Formula presented.) topological equivalences.

Original language	Spanish
Pages (from-to)	176-191
Number of pages	16
Journal	Journal of Topology
Volume	16
State	Published - 6 Feb 2023

Cite this

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title = "On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance",

abstract = "We define the Milnor number of a one-dimensional holomorphic foliation (Formula presented.) as the intersection number of two holomorphic sections with respect to a compact connected component (Formula presented.) of its singular set. Under certain conditions, we prove that the Milnor number of (Formula presented.) on a three-dimensional manifold with respect to (Formula presented.) is invariant by (Formula presented.) topological equivalences.",

author = "Arturo Fern{\'a}ndez-P{\'e}rez and Costa, {Gilcione Nonato} and Rudy Rosas",

year = "2023",

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T1 - On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance

AU - Fernández-Pérez, Arturo

AU - Costa, Gilcione Nonato

AU - Rosas, Rudy

PY - 2023/2/6

Y1 - 2023/2/6

N2 - We define the Milnor number of a one-dimensional holomorphic foliation (Formula presented.) as the intersection number of two holomorphic sections with respect to a compact connected component (Formula presented.) of its singular set. Under certain conditions, we prove that the Milnor number of (Formula presented.) on a three-dimensional manifold with respect to (Formula presented.) is invariant by (Formula presented.) topological equivalences.

AB - We define the Milnor number of a one-dimensional holomorphic foliation (Formula presented.) as the intersection number of two holomorphic sections with respect to a compact connected component (Formula presented.) of its singular set. Under certain conditions, we prove that the Milnor number of (Formula presented.) on a three-dimensional manifold with respect to (Formula presented.) is invariant by (Formula presented.) topological equivalences.

UR - https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/topo.12281

M3 - Artículo

SN - 1753-8416

VL - 16

SP - 176

EP - 191

JO - Journal of Topology

JF - Journal of Topology

ER -

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

Abstract

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