Topological Moduli Space for Germs of Holomorphic Foliations
Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mattei, Jean-François (Institut de Mathématiques de Toulouse)
Salem, Eliane (Sorbonne Université. Institut de Mathématiques de Jussieu-Paris Rive Gauche)

Date:	2020
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.
Grants:	Ministerio de Economía y Competitividad MTM2011-26674-C02-01 Ministerio de Economía y Competitividad MTM2015-66165-P Ministerio de Economía y Competitividad MDM-2014-0445
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Complex dynamical systems ; Singular foliations ; Holonomy ; Topological invariants ; Teichmüller space ; Moduli space ; Non-abelian cohomology
Published in:	International Mathematics Research Notices, Vol. 2020, Issue 23 (November 2020) , p. 9228-9292, ISSN 1687-0247

DOI: 10.1093/imrn/rny244

54 p, 1.0 MB

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