The Seiberg–Witten equations and the Weinstein conjecture

2006/11/30 by Clifford Henry Taubes · 141 citations
Mathematics · #Conjecture #Field (mathematics) #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Kernel (algebra) #Manifold (fluid mechanics) #Nonlinear Partial Differential Equations #Vector field #math.GT #math.SG #msc:57R17 #msc:57R57

paper · pdf · doi:10.2140/gt.2007.11.2117

published in Geometry & Topology 11(4), 2117-2202 (Mathematical Sciences Publishers) · This new version has some minor corrections

arxiv created 2007/02/16 · openalex publication_date 2007/10/15 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Let M denote a compact, oriented 3-dimensional manifold and let a denote a contact 1-form on M ; thus a^da is nowhere zero. This article proves that the vector field that generates the kernel of da has a closed integral curve.

Citations

• Rounding corners of polygons and the embedded contact homology ofT3
• Le Spectre d’une Variété Riemannienne

Cited by

• Computable functions as Reeb flows
• Conformally symplectic topology from a dynamical viewpoint
• Closed Reeb orbits on contact type hypersurfaces in T^*Sⁿ
• Bott-integrable contact forms with large systolic ratio
• A Short History of the Weinstein Conjecture
• Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions
• Embedded contact homology and Seiberg–Witten Floer cohomology I
• Symplectic Floer homology of area-preserving surface diffeomorphisms
• Planarity in Higher-Dimensional Contact Manifolds
• Pin(2)-equivariant Seiberg–Witten Floer homology of Seifert fibrations
• Clifford Taubes [wikipedia]
• Floer homology [wikipedia]