Abstract
A codimension q-foliation is a partition of a manifold into submanifolds that locally looks like the fibers of a submersion onto the Euclidean space of dimension q. Foliations come with cohomological invariants – the most famous one being the Godbillon-Vey invariant/Thurston’s “helical wobble” for codimension 1 foliations. We are going to present a modern version of Haefliger’s construction of a characteristic map for foliations – organizing these invariants into a universal object. We will talk about groupoids, classifying spaces for groupoid principal actions, jet spaces and their canonical distribution, and the “Chern-Weil” construction of characteristic classes for foliations.