Monodromy and topological classification of germs of holomorphic foliations

TL;DR

This paper provides a comprehensive topological classification of germs of holomorphic foliations in the plane, introducing a new invariant called monodromy representation that captures essential dynamical features.

Contribution

It introduces the monodromy representation as a new topological invariant and proves the topological invariance of the projective holonomy representation under generic conditions.

Findings

Complete topological classification achieved

Monodromy representation encodes key dynamical information

Topological invariance of projective holonomy confirmed

Abstract

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.