Tangential category of foliations
type: Item
instance of: scholarly article
title: Tangential category of foliations
zbMATH Open document ID: 1026.55004
DOI: 10.1016/S0040-9383(02)00021-6
published in: Topology
publication date: 2003-06-17T00:00:00Z
review text: The notion of tangential Ljusternik-Schnirelman category for foliations was introduced by Helen Colman in her thesis. The authors obtain some estimates for tangential category and prove that the tangential category is upper semicontinuous with respect to foliations. As an application, we mention here the following result (Theorem 7.2): Let \(\mathcal F\) be a \(C^2\)-foliation of codimension 1 on a closed manifold \(M\) of dimension \(n\geq 3\). Then the tangential category of \(\mathcal F\) is at most 1 if and only if the leaves of \(F\) are the fibers of a homotopy sphere bundle over \(S^1\).
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 1929318
zbMATH Keywords: foliations
zbMATH Keywords: Ljusternik-Schnirelman category
author: Wilhelm Singhof
author: Elmar Vogt
reviewed by: Yuli Rudyak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1929318