Contact structures on 3-manifolds are deformations of foliations

2006/07/31 by John B. Etnyre, Etnyre, John B.
Mathematics · #57R17 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0607825

openalex publication_date 2006/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we observe, answering a question of Eliashberg and Thurston, that all contact structures on a closed oriented 3-manifold are C^∞-deformations of foliations.

Related

• Foliations, contact structures and their interactions in dimension three
• On Legendrian foliations in contact manifolds II: Deformation theory
• Approximating C^1,0-foliations
• C⁰-Contact Geometry of Surfaces in 3-Manifolds
• Taut foliations and contact pairs in dimension three