Non-unimodular transversely homogeneous foliations

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the ambient manifold, the closure of the leaves or the total space of an associated principal bundle fiber over $S^1$.

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