Optimal positioning of tori with respect to an Anosov flow
type: Item
instance of: scholarly article
title: Optimal positioning of tori with respect to an Anosov flow
zbMATH Open document ID: 0838.58029
DOI: 10.1007/BF02566001
author: Thierry Barbot
published in: Commentarii Mathematici Helvetici
publication date: 1996-06-06T00:00:00Z
full work available at URL: https://eudml.org/doc/140363
review text: Anosov flows on 3-manifolds are studied via their incompressible tori. A technical term is ``optimal position'' of such a torus, which essentially means that it is isotopic to a torus transverse to the flow outside finitely many closed orbits. Homotopic tori in optimal position are homotopic along the flow. A topological condition is given that guarantees that a torus can be isotoped to one in optimal position. If finitely many disjoint tori can separately be deformed to tori in optimal position then the latter can be chosen to be disjoint. An important role in the geometric analysis of a Birkhoff annulus in such an Anosov flow is played by ``lined up lozenges'' (chapelet de losanges - diamond shaped pieces chained up in a row), a subset in the orbit space of the universal cover of the 3-manifold by the canonical 1-dimensional foliation.
reviewed by: Dieter Erle
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 791087
zbMATH Keywords: foliation
zbMATH Keywords: Birkhoff annulus
zbMATH Keywords: quasi-transverse torus
zbMATH Keywords: incompressible torus
zbMATH Keywords: incompressible Klein bottle
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 791087