  We show that if the structure algebra of a Riemannian foliation F on a closed
manifold M is nilpotent, then the integral of the \'Alvarez class of (M,F)
along every closed path is the exponential of an algebraic number. By this
result and the continuity of the \'Alvarez class under deformations shown in
arXiv:1009.1098v2, we prove that the \'Alvarez class and the geometrically
tautness of Riemannian foliations on a closed manifold M are invariant under
deformation, if the fundamental group of M has polynomial growth.
