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arXiv · 0909.1125

Rigidity of the Alvarez class

Hiraku Nozawa
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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 $π_{1}M$ is polycyclic or $\mathcal{F}$ is of polynomial growth.

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Hiraku Nozawa. 2010-09-06. Rigidity of the Alvarez class. https://doi.org/10.1007/s00229-010-0347-3

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