Topological moduli space for germs of holomorphic foliations

2017/05/15 by Marín, David, Mattei, Jean-François, Salem, Éliane
#32S50 #32S65 #34M #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F75 #Secondary 32M25

paper · doi:10.48550/arxiv.1705.05258

Abstract

This work deals with the topological classification of germs of singular foliations on (\mathbb C²,0). 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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