Transversal Whitney Topology and Singularities of Haefliger Foliations

In order to study singularities of Haefliger foliation, we define the notion of transversally Whitney C ^∞-topology modulo a regular foliation on the set of C ^∞-mappings into a foliated manifold. We prove a kind of transversality theorem with respect to this new topology. All arguments we use here are analogous to those of the theory for the ordinary Whitney C ^∞-topology. However, this is the first attempt for the study of generic properties of Haefliger foliations

Dedicated to the memory of Professor Luiz A. Faνaro