Category and compact leaves (Q2498040)

For the definition of transverse saturated Lusternik--Schnirelmann (in future LS) category for a foliated manifold, see \textit{H. Colman} and \textit{S. Hurder} [Trans. Am. Math. Soc. 356, No. 4, 1463--1487 (2004; Zbl 1038.55003)]. The author proves that that if a \(C^1\)-foliated manifold has finite transverse saturated LS category then the foliation has a compact leaf. Furthermore, such a foliation is not expansive on any of its non-trivial minimal sets.