Rigidity of the Alvarez class

Details Rigidity of the Alvarez class Rigidity of the Alvarez class

2009-09-07

arxiv.org/abs/0909.1125v3

Manuscripta Math. 132 (1), 257-270 (2010)

Mathematics

Differential Geometry

13 pages, correction of misprints

Scientific paper

10.1007/s00229-010-0347-3

Let $(M,\mathcal{F})$ be a closed manifold with a Riemannian foliation. The \'{A}lvarez 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 \'{A}lvarez 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.

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