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arXiv · 1705.05258

Topological moduli space for germs of holomorphic foliations

David Marín·Jean-François Mattei·Éliane Salem
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Abstract

This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and the projective holonomy representations and we compute the moduli space of topological classes in terms of the cohomology of a new algebraic object that we call group-graph. This moduli space may be an infinite dimensional functional space but under generic conditions we prove that it has finite dimension and we describe its algebraic and topological structures.

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David Marín, Jean-François Mattei, Éliane Salem. 2017-09-18. Topological moduli space for germs of holomorphic foliations. https://arxiv.org/abs/1705.05258

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