Monodromy and topological classification of germs of holomorphic foliations

David Marín, Jean-François Mattei

Published 2010-04-09, updated 2012-06-11Version 3

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representation whose topological invariance was conjectured in the eighties by Cerveau and Sad and proved here under mild hypotheses.