Vector fields with transverse foliations
type: Item
instance of: scholarly article
title: Vector fields with transverse foliations
zbMATH Open document ID: 0581.57014
DOI: 10.1016/0040-9383(85)90005-9
author: Sue Goodman
published in: Topology
publication date: 1985-01-01T00:00:00Z
review text: In any homotopy class of nonsingular vector fields of any closed oriented n-manifold there is an open set with no transverse foliation. For \(n=3\) this follows from the failure of a linking property which is a necessary condition for the flow to have a transverse foliation. The author shows that for a nonsingular Morse-Smale flow on a closed oriented 3-manifold the linking property is also a sufficient condition.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 37D15
zbMATH DE Number: 3929961
zbMATH Keywords: homotopy class of nonsingular vector fields
zbMATH Keywords: transverse foliation
zbMATH Keywords: nonsingular Morse-Smale flow on a closed oriented 3-manifold
zbMATH Keywords: linking property
MaRDI profile type: Publication
full work available at URL: 0040-9383(85)90005-9
OpenAlex ID: W1979236904
Wikidata QID: Q126377301
description: scientific article; zbMATH DE number 3929961