Hurder, Steven; Walczak, Paweł G. Compact foliations with finite transverse LS category. (English) Zbl 1404.57046 J. Math. Soc. Japan 70, No. 3, 1015-1046 (2018). Main results (Corollary 1.3): Let \(\mathcal F\) be a compact \(C^1\)-foliation of a compact manifold \(M\). If \(M\) admits a covering by transversely categorical open saturated sets, then \(\mathcal F\) is compact Hausdorff.This corollary follows from a technical Theorem 1.2 asserting that there is no transversely saturated covering of so-called bad spaces. Reviewer: Yuli Rudyak (Gainesville) Cited in 4 Documents MSC: 57R30 Foliations in differential topology; geometric theory 53C12 Foliations (differential geometric aspects) 55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects) 57S15 Compact Lie groups of differentiable transformations Keywords:compact foliation; transverse Lusternik-Schnirelmann category; Epstein filtration PDF BibTeX XML Cite \textit{S. Hurder} and \textit{P. G. Walczak}, J. Math. Soc. Japan 70, No. 3, 1015--1046 (2018; Zbl 1404.57046) Full Text: DOI arXiv OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.