Tight contact structures and Anosov flows
type: Item
instance of: scholarly article
title: Tight contact structures and Anosov flows
zbMATH Open document ID: 1028.53080
DOI: 10.1016/S0166-8641(01)00232-2
author: John B. Etnyre
author: Robert Ghrist
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: In this paper, the authors observe a relationship between tight contact structures and Anosov flows on \(3\)-manifolds. A key tool is the result of \textit{Y. Mitsumatsu} [Ann. Inst. Fourier 45, 1407-1421 (1995; Zbl 0834.53031)] that the generator of an Anosov flow on a compact \(3\)-manifold is contained in the intersection of a pair of tight contact structures. Using this and Gompf's \(3\)-manifold invariant \(\theta\), they obtain a simple (up to these prerequisites) proof of the fact that \(S^3\) has no Anosov flows. Some other questions are also considered.
Mathematics Subject Classification ID: 53D35
Mathematics Subject Classification ID: 37D20
zbMATH DE Number: 1879094
zbMATH Keywords: contact manifold
zbMATH Keywords: Anosov flow
reviewed by: John Oprea
MaRDI profile type: Publication
Wikidata QID: Q125291293
cites work: Q3692516
cites work: Classification of overtwisted contact structures on 3-manifolds
cites work: Contact 3-manifolds twenty years since J. Martinet's work
cites work: Q3357032
cites work: Q4375270
cites work: Symplectic convexity in low-dimensional topology
cites work: Tight contact structures on lens spaces
cites work: Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture
cites work: On the nonexistence of tight contact structures
cites work: Q3914116
cites work: An infinity of tight contact structures on an infinity of manifolds
cites work: Foliations: geometric studies
cites work: Handlebody construction of Stein surfaces
cites work: Pseudo holomorphic curves in symplectic manifolds
cites work: Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three
cites work: The dynamics on three-dimensional strictly convex energy surfaces
cites work: On the classification of tight contact structures. I
cites work: The topology of 4-manifolds
cites work: Monopoles and contact structures
cites work: Noninvolutory Hopf algebras and \(3\)-manifold invariants
cites work: Tight contact structures and Seiberg-Witten invariants
cites work: Corrigenda to: Introduction to Symplectic Topology
cites work: Anosov flows and non-Stein symplectic manifolds
cites work: Anosov Flows
cites work: Anosov flows and the fundamental group
cites work: An obstruction to sliceness via contact geometry and ``classical'' gauge theory
full work available at URL: s0166-8641(01)00232-2
OpenAlex ID: W2078137657
description: scientific article; zbMATH DE number 1879094