One sided branching in Anosov foliations
type: Item
instance of: scholarly article
title: One sided branching in Anosov foliations
zbMATH Open document ID: 0885.58071
DOI: 10.1007/BF02566007
author: Sergio R. Fenley
published in: Commentarii Mathematici Helvetici
publication date: 1997-12-16T00:00:00Z
full work available at URL: https://eudml.org/doc/140368
review text: Let \({\mathcal F}^s\) and \({\mathcal F}^u\) be the stable and unstable 2-dimensional (Anosov) foliations of the Anosov flow \(\Phi\) on \(M^3\) and \(\widetilde{\mathcal F}^s\), \(\widetilde{\mathcal F}^u\) the respective lifts to the universal cover. Their leaf spaces are 1-dimensional manifolds, if they are Hausdorff then they are homeomorphic to the real line \(\mathcal R\), otherwise we say that the foliation has branching. We say that \(\widetilde{\mathcal F}^s\) (or \(\widetilde{\mathcal F}^u\)) has one sided branching if its leaf space is not \(\mathcal R\) but the branching occurs only in the positive (or negative) transversal direction. Main theorem: Let \(\Phi\) be a topological transitive Anosov flow in \(M^3\). If one of \(\widetilde{\mathcal F}^s\) or \(\widetilde{\mathcal F}^u\) has branching then both \(\widetilde{\mathcal F}^s\) or \(\widetilde{\mathcal F}^u\) have branching in the positive and negative directions.
reviewed by: Tomasz Nowicki
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 790581
zbMATH Keywords: Anosov flow
zbMATH Keywords: 3-manifolds
zbMATH Keywords: lifts
zbMATH Keywords: branching
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 790581