Rigidity of the Alvarez class

Original · EN

Let (M,F) be a closed manifold with a Riemannian foliation. The Álvarez class is the cohomology class of degree 1 of M whose triviality characterizes the minimizability of (M,F). We show that the integral of the Álvarez class along every closed path in M is the logarism of an algebraic integer if π₁M is polycyclic or F is of polynomial growth.