Knot homology groups from instantons

2008/06/30 by P. B. Kronheimer, Tomasz Mrowka, T. S. Mrowka · 3 citations
Computer Science · Mathematics · #Citation #Combinatorics #Computer science #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Library science #Mathematics #Subject (documents) #Topological and Geometric Data Analysis #math.GT #msc:57M25 #msc:57R58

paper · pdf · doi:10.1112/jtopol/jtr024

118 pages, 1 figure. v2: Further acknowledgements

arxiv created 2008/08/01 · openalex publication_date 2011/11/29 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology.

Citations

• Floer homology and knot complements
• The orientation of Yang-Mills moduli spaces and 4-manifold topology
• Holomorphic disks and knot invariants
• A slice genus lower bound from sl(n) Khovanov–Rozansky homology
• Quantum field theory and the Jones polynomial
• A categorification of the Jones polynomial
• Some differentials on Khovanov-Rozansky homology
• Matrix factorizations and link homology

Cited by

• Khovanov homology is an unknot-detector
• Surface defects and resolvents
• Traceless SU(2) representations of 2-stranded tangles

Related

• Knots, sutures and excision
• Some Computations on Instanton Knot Homology
• On Heegaard Floer minimal knots in sutured manifolds
• Symplectic instanton knot homology
• Knot surgery formulae for instanton Floer homology II: applications