Non-unimodular transversely homogeneous foliations

TL;DR

This paper establishes conditions for tautness in transversely homogeneous foliations on compact manifolds and explores implications of non-unimodularity, including fiber bundle structures over the circle.

Contribution

It provides new criteria for tautness based on base-like cohomology and links non-unimodularity to fiber bundle structures over $S^1$.

Findings

Tautness characterized by base-like cohomology.

Non-unimodular foliations imply fiber bundle structures over $S^1$.

Conditions connect foliation properties with manifold topology.

Abstract

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 $S^1$.