Extended Holonomy and Topological Invariance of Vanishing Holonomy Group

In this work, we introduce the notion of extended holonomy and discuss some of its properties. As an application of it, we consider vanishing projective holonomy groups of germs of vector fields with zero (n???1)-jet and prove, under some genericity assumptions, that the corresponding vanishing holonomy groups are topologically conjugated for orbitally topologically equivalent germs of vector fields.