Codimension one minimal foliations and the fundamental groups of leaves
type: Item
instance of: scholarly article
title: Codimension one minimal foliations and the fundamental groups of leaves
zbMATH Open document ID: 1148.53017
author: Tomoo Yokoyama
author: Takashi Tsuboi
publication date: 2008-07-04T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10330
review text: The authors study codimension one, transversely orientable, real-analytic foliations of a paracompact manifold for which every leaf is dense. Under these conditions, they prove that the foliation is without holonomy if either (1) the fundamental group of every leaf is isomorphic to \({\mathbb Z}\) or (2) the 2nd homotopy group of the ambient manifold is zero and the fundamental group of every leaf is isomorphic to \({\mathbb Z}^k\) for some \(k \geq 0\). They remark that the assumption of real-analyticity is there solely to guarantee that there are no null homotopic closed transverse curves to the foliation. An example is given to show the necessity of the denseness of the leaves. They also construct an example of a foliation with nontrivial holonomy with diffeomorphic leaves.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 5298318
zbMATH Keywords: foliations
zbMATH Keywords: real-analytic
zbMATH Keywords: holonomy
zbMATH Keywords: fundamental group of leaves
reviewed by: James Hebda
MaRDI profile type: Publication
OpenAlex ID: W2492799441
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DOI: 10.5802/AIF.2366
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5298318