Expansive foliations (Q1190705)

The authors introduce the notion of expansiveness into foliation theory. They prove that in the case of codimension-one foliations the topological structure of a foliation completely characterizes its expansiveness. It follows that the geometric entropy of a codimension-one expansive foliation is positive and that the fundamental group of a manifold admitting a codimension-one expansive foliation has exponential growth. Similar results are obtained in the case of strongly expansive foliations with arbitrary codimension.