Topological Moduli Space for Germs of Holomorphic Foliations

David Marín*, Jean François Mattei, Éliane Salem

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

Abstract

This work deals with the topological classification of germs of singular foliations on (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 structure.

Original languageAmerican English
Pages (from-to)9228-9292
Number of pages65
JournalInternational Mathematics Research Notices
Volume2020
Issue number23
DOIs
Publication statusPublished - 1 Nov 2020

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