Incompressibilité des feuilles de germes de feuilletages holomorphes singuliers

David Marín, Jean François Mattei

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

We consider a non-dicritic germ of singular holomorphic foliation F defined in some closed ball B̄ ⊂ ℂ2 with separatrix set S, satisfying some additional but generic hypotheses. We prove that there exists an open subset U ⊃ S of B, such that for every leaf L of F (U\U) the natural inclusion i: L {right arrow, hooked} U \ S induces a monomorphism i*: π1, (L) {right arrow, hooked} π1, (U \ S) at the fundamental group level. To do this, we introduce the geometrical notion of "foliated connexity: and we re-interpret the incompressibility using it. We also show the existence of some special transverse holomorphic sections, which allow us to introduce a "global monodromy representation" for the foliation. © 2008 Société Mathématique de France.
Original languageEnglish
Pages (from-to)855-903
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume41
Issue number6
DOIs
Publication statusPublished - 1 Jan 2008

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