Topological moduli space for germs of foliations II : universal deformations
Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mattei, Jean-François (Université Paul Sabatier. Institut de Mathématiques de Toulouse)
Salem, Eliane (Sorbonne Université. Institut de Mathématiques de Jussieu-Paris Rive Gauche)

Data:	2023
Resum:	This work deals with the topological classification of singular foliation germs 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 prove the existence of a topological universal deformation through which every equisingular deformation uniquely factorizes up to topological conjugacy. This is done by representing the functor of topological classes of equisingular deformations of a fixed foliation. We also describe the functorial dependence of this representation with respect to the foliation.
Ajuts:	Agencia Estatal de Investigación PGC2018-095998-B-I00 Agencia Estatal de Investigación PID2021-125625NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1725 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-01015
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Complex dynamical systems ; Complex ordinary differential equations ; Holomorphic vector fields ; Singular foliations ; Holonomy ; Universal deformations ; Representable functors ; Non abelian cohomology
Publicat a:	Annali della Scuola normale superiore di Pisa - Classe di scienze, In press 2023, ISSN 0391-173X

Adreça alternativa: https://journals.sns.it/index.php/annaliscienze/article/view/5925
DOI: 10.2422/2036-2145.202111_006

Postprint 53 p, 1.1 MB

El registre apareix a les col·leccions:
Articles > Articles de recerca
Articles > Articles publicats