Georges Habib
We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant.We also show that foliated homotopic maps between Riemannian foliations induce isomorphic maps on basic Lichnerowicz cohomology, and that the Alvarez class of a Riemannian foliation is invariant under foliated homotopy equivalence. This is a joint work with Ken Richardson.
