Embedded contact homology and Seiberg–Witten Floer cohomology I

2010/12/15 by Clifford Henry Taubes · 119 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Floer homology #Mathematics #Cohomology #Pure mathematics #Morse homology #Mayer–Vietoris sequence #Isomorphism (crystallography) #Homology (biology) #Khovanov homology #Algebra over a field #Equivariant cohomology #Cellular homology #De Rham cohomology #Symplectic geometry #Crystallography

paper · pdf · doi:10.2140/gt.2010.14.2497

published in Geometry & Topology 14(5), 2497-2581 (Mathematical Sciences Publishers)

openalex publication_date 2010/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/24

Abstract

This is the first of five papers that construct an isomorphism between the embedded contact homology and Seiberg-Witten Floer cohomology of a compact 3-manifold with a given contact 1-form. This paper describes what is involved in the construction.

Citations

• Morse theory for Lagrangian intersections
• The Seiberg–Witten equations and the Weinstein conjecture
• ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations
• Rounding corners of polygons and the embedded contact homology ofT3
• Embedded contact homology and Seiberg-Witten Floer cohomology I

Cited by

• Symplectic Floer homology of area-preserving surface diffeomorphisms
• Ehrhart functions and symplectic embeddings of ellipsoids
• Recent progress on symplectic embedding problems in four dimensions
• On the monopole Lefschetz number of finite-order diffeomorphisms
• Clifford Taubes [wikipedia]