# Homotopy invariance of cohomology and signature of a Riemannian foliation. Part 1/2

#### 07.07.2017, 11:00  –  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.

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