Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 70, Number 3 (2018), 1015-1046.
Compact foliations with finite transverse LS category
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.
J. Math. Soc. Japan, Volume 70, Number 3 (2018), 1015-1046.
Received: 9 December 2016
First available in Project Euclid: 12 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R30: Foliations; geometric theory 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space
Secondary: 57S15: Compact Lie groups of differentiable transformations
HURDER, Steven; WALCZAK, Paweł. Compact foliations with finite transverse LS category. J. Math. Soc. Japan 70 (2018), no. 3, 1015--1046. doi:10.2969/jmsj/76837683. https://projecteuclid.org/euclid.jmsj/1528790547