HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology

2010/07/31 by Çağatay Kutluhan, Cagatay Kutluhan, Yi‐Jen Lee +2 · 125 citations
Mathematics · Medicine · #Algebra over a field #Amino acid #Botulinum Toxin and Related Neurological Disorders #Cellular homology #Combinatorics #Crystallography #Fibered knot #Floer homology #Genetics #Geometric and Algebraic Topology #Heegaard splitting #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Khovanov homology #Mathematics #Morse homology #Pure mathematics #math.GT #math.SG

paper · pdf · doi:10.2140/gt.2020.24.2829

published in Geometry & Topology 24(6), 2829-2854 (Mathematical Sciences Publishers) · 25 pages. This version includes a minor revision to Theorem 3.3

arxiv created 2011/07/12 · openalex publication_date 2020/12/29 · arxiv updated 2021/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups of M.

Citations

• Holomorphic disks and three-manifolds invariants: Properties and applications
• Holomorphic disks and topological invariants for closed three-manifolds
• Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions
• Periodic Floer pro-spectra from the Seiberg-Witten equations
• Rounding corners of polygons and the embedded contact homology ofT3

Cited by

• On the monopole Lefschetz number of finite-order diffeomorphisms
• Knot Floer homology of positive braids
• Clifford Taubes [wikipedia]
• Floer homology [wikipedia]

Related

• HF=HM V: Seiberg-Witten-Floer homology and handle addition
• An algorithm to compute some Heegaard Floer homologies
• Topics in Heegaard Floer homology
• The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
• Heegaard Floer homology for manifolds with torus boundary: properties and examples