Transverse Lusternik-Schnirelmann category of Riemannian foliations
type: Item
instance of: scholarly article
title: Transverse Lusternik-Schnirelmann category of Riemannian foliations
zbMATH Open document ID: 1052.55005
author: Hellen Colman
published in: Topology and its Applications
publication date: 2004-08-20T00:00:00Z
review text: The transverse Lusternik-Schnirelmann category of a foliation is an invariant of foliated homotopy type that has been introduced by H. Colman and E. Macias. Let \((M,{\mathcal F})\) and \((M',{\mathcal F}')\) be foliated manifolds. A homotopy \(H : M\times M'\) is foliated if for each \(t\in I\), the map \(H_t\) sends each leaf of \(\mathcal {\mathcal F}\) into another leaf of \({\mathcal F}'\). An open subset \(U\subset M\) is called transversely categorical if there is a foliated homotopy \(H : U\times I\to M\) such that \(H_0: U \to M\) is the inclusion map and the image of \(H_1\) is contained in a single leaf of \(\mathcal F\). The transverse LS category is the least integer \(k\) such that \(M\) may be covered by \(k\) open saturated transversely categorical subsets in \(M\). In this paper, the author shows that the category is infinite if there exists a non-compact leaf that verifies a certain condition. Explicit examples are given.
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 2093559
zbMATH Keywords: LS category
zbMATH Keywords: foliations
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: j.topol.2003.12.006
OpenAlex ID: W2074719734
Wikidata QID: Q115340868
cites work: Q3687366
cites work: Q3702972
cites work: Q5316738
cites work: Q3147737
cites work: LS-category of compact Hausdorff foliations
cites work: Transverse Lusternik-Schnirelmann category of foliated manifolds
cites work: Q4421932
cites work: Q3687365
cites work: Holonomy groupoids of singular foliations.
cites work: Foliations with all leaves compact
cites work: Q3696075
cites work: Category and compact leaves
cites work: Compact foliations with finite transverse LS category
cites work: Fibrewise category
cites work: A G-Lusternik-Schnirelmann category of space with an action of a compact Lie group
cites work: Riemannian foliations. With appendices by G. Cairns, Y. Carrière, E. Ghys, E. Salem, V. Sergiescu
cites work: Q5816023
cites work: Accessible Sets, Orbits, and Foliations with Singularities
cites work: Orbits of Families of Vector Fields and Integrability of Distributions
DOI: 10.1016/J.TOPOL.2003.12.006
description: scientific article; zbMATH DE number 2093559