\(C^ 1\) foliations which cannot be approximated by \(C^ 2\) foliations
type: Item
instance of: scholarly article
title: \(C^ 1\) foliations which cannot be approximated by \(C^ 2\) foliations
zbMATH Open document ID: 0647.57020
author: Koichi Yano
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: Let M be a closed manifold and \(\tau\) be a homotopy class of codimension k plane fields on M. Define \(Fol^ r_{\tau}(M)\) to be the space of the codimension k foliations of class \(C^ r\) of M whose tangent bundles are in \(\tau\). In \(Fol^ r_{\tau}(M)\) consider the \(C^ 0\) or \(C^ 1\) topology. The author shows that if dim M\(>2\) and \(\chi (M)=0\), then for any homotopy class \(\tau\) of codimension one plane fields on M, \(Fol^ 2_{\tau}(M)\) is not dense in \(Fol^ 1_{\tau}(M)\) with respect to the \(C^ 0\) topology. If \(\tau\) is a homotopy class of plane fields of codimension greater than one, then \(Fol^ 2_{\tau}(M)\) is note dense in \(Fol^ 1_{\tau}(M)\) with respect to the \(C^ 1\) topology.
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4056591
zbMATH Keywords: topologically conjugate foliations
zbMATH Keywords: approximating \(C^ 2\)-foliations by \(C^ 1\)-foliations
zbMATH Keywords: space of the codimension k foliations of class \(C^ r\)
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228080
OpenAlex ID: W2079363750
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DOI: 10.2748/TMJ/1178228080
description: scientific article; zbMATH DE number 4056591