In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of holonomy transformation. Unlike the regular case, holonomy transformations cannot be attached to classes of paths in the foliation, but rather to elements of the holonomy groupoid of the singular foliation.
National and Kapodistrian University of Athens, Department of Mathematics (+30) 210-7276423 Panepistimiopolis Zografou Athens, ZipCode 157-84 iandroul@math.uoa.gr
