Rigidity of the Alvarez class

Abstract

Let $(M,\mathcal{F})$ 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 $(M,\mathcal{F})$. We show that the integral of the Álvarez class along every closed path in $M$ is the logarism of an algebraic integer if ${\pi }_{1}M$ is polycyclic or $\mathcal{F}$ is of polynomial growth.

13 pages, correction of misprints

References in corpus (2)

• Deformation of Sasakian metrics
• Rigidity of the Álvarez classes of Riemannian foliations with nilpotent structure Lie algebras

Cited by in corpus (6)

• Modified differentials and basic cohomology for Riemannian foliations
• Minimizability of developable Riemannian foliations
• Continuity of the Alvarez class under deformations
• Cohomological Tautness of Singular Riemannian Foliations
• Homotopy invariance of cohomology and signature of a riemannian foliation
• Tenseness of Riemannian flows