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Compact foliations with finite transverse LS category. (English) Zbl 1404.57046

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.

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
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