Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions

2011/04/27 by Vincent Colin, Paolo Ghiggini, Ko Honda · 3 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics #Floer homology #Morse homology #Homology (biology) #Mathematics #Equivalence (formal languages) #Pure mathematics #Sketch #Cellular homology #Combinatorics #Algebra over a field #Symplectic geometry #Algorithm #Amino acid #Biology #Genetics

paper · pdf · doi:10.1073/pnas.1018734108

openalex publication_date 2011/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We sketch the proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology (ECH). The key point is to express these two Floer homology theories in terms of an open book decomposition of the ambient manifold.

Citations

• Embedded contact homology and open book decompositions
• Holomorphic disks and knot invariants
• Holomorphic disks and three-manifolds invariants: Properties and applications
• The Seiberg–Witten equations and the Weinstein conjecture
• Holomorphic disks and topological invariants for closed three-manifolds
• Knot Floer homology detects fibred knots

Cited by

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• On the monopole Lefschetz number of finite-order diffeomorphisms
• Pin(2)-equivariant Seiberg–Witten Floer homology of Seifert fibrations
• Floer homology [wikipedia]

Related

• HF = ECH via open book decompositions: a summary
• The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
• Embedded contact homology and open book decompositions
• The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology