Topology of singular holomorphic foliations along a compact divisor

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(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mattei, Jean-François (Institut de Mathématiques de Toulouse)

Data:	2014
Resum:	We consider a singular holomorphic foliation F defined near a compact curve C of a complex surface. Under some hypothesis on (F;C) we prove that there exists a system of tubular neighborhoods U of a curve D containing C such that every leaf L of Fj(U\D) is incompressible in U\D. We also construct a representation of the fundamental group of the complementary of D into a suitable automorphism group, which allows to state the topological classication of the germ of (F;D), under the additional but generic dynamical hypothesis of transverse rigidity. In particular, we show that every topological conjugation between such germs of holomorphic foliations can be deformed to extend to the exceptional divisor of their reductions of singularities.
Ajuts:	Ministerio de Economía y Competitividad MTM2008-02294 Ministerio de Economía y Competitividad MTM2011-26674-C02-01
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Holomorphic foliations
Publicat a:	Journal of singularities, Vol. 9 (2014) , p. 122-150, ISSN 1949-2006

29 p, 982.5 KB

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