Constructing equivalences with some extensions to the divisor and topological invariance of projective holonomy

Abstract

Given topologically equivalent germs of holomorphic foliations $\mathcal{F}$ and ${\mathcal{F}}^{\prime }$, under some hypothesis, we construct topological equivalences extending to some regions of the divisor after resolution of singularities. As an application we study the topological invariance of the projective holonomy representation.