Homotopy invariance of cohomology and signature of a Riemannian foliation. Part 2

12.07.2017, 10:30  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

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.