Open Access
July, 2018 Compact foliations with finite transverse LS category
J. Math. Soc. Japan 70(3): 1015-1046 (July, 2018). DOI: 10.2969/jmsj/76837683


We prove that if $F$ is a foliation of a compact manifold $M$ with all leaves compact submanifolds, and the transverse saturated category of $F$ is finite, then the leaf space $M/F$ is compact Hausdorff. The proof is surprisingly delicate, and is based on some new observations about the geometry of compact foliations. The transverse saturated category of a compact Hausdorff foliation is always finite, so we obtain a new characterization of the compact Hausdorff foliations among the compact foliations as those with finite transverse saturated category.


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Steven HURDER. Paweł WALCZAK. "Compact foliations with finite transverse LS category." J. Math. Soc. Japan 70 (3) 1015 - 1046, July, 2018.


Received: 9 December 2016; Published: July, 2018
First available in Project Euclid: 12 June 2018

zbMATH: 06966972
MathSciNet: MR3830797
Digital Object Identifier: 10.2969/jmsj/76837683

Primary: 53C12 , 55M30 , 57R30
Secondary: 57S15

Keywords: compact foliation , Epstein filtration , transverse Lusternik–Schnirelmann category

Rights: Copyright © 2018 Mathematical Society of Japan

Vol.70 • No. 3 • July, 2018
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