Topics on Lie pseudogroups : Pfaffian groups, Haefliger's cohomology and natural bundles

Abstract

This thesis deals with Lie pseudogroups. Lie pseudogroups are a modern version of the "continuous transformation groups" introduced by Sophus Lie in collaboration with Friedrich Engel. They are, roughly speaking, sets of local transformations of manifolds satisfying some group-like and sheaf-like properties and arising as sets of (local) solutions of some system of partial differential equations. They often arise as the sets of local symmetries of some geometric structures. In this thesis we made use of some modern geometric tools to review, investigate and generalize some classical results on pseudogroups, geometric structures and related matters.