Abstract
Let \({(M,\mathcal{F})}\) be a closed manifold with a Riemannian foliation. The Álvarez class of \({(M,\mathcal{F})}\) is a cohomology class of M of degree 1 whose triviality characterizes the minimizability or the geometrically tautness of \({(M,\mathcal{F})}\) . We show that the integral of the Álvarez class of \({(M,\mathcal{F})}\) along every closed path is the logarithm of an algebraic integer if π1 M is polycyclic or \({\mathcal{F}}\) is of polynomial growth.
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