2018/01/31 by John A. Baldwin, Steven Sivek
Mathematics · Medicine · #Algebra over a field #Biology #Botulinum Toxin and Related Neurological Disorders #Cellular homology #Cohomology #Combinatorics #Floer homology #Genetics #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Instanton #Khovanov homology #Knot (papermaking) #Mathematical physics #Mathematics #Morse homology #Pure mathematics #Spectral sequence #Symplectic geometry #math.GT #math.SG
paper · pdf · doi:10.1215/00127094-2021-0034
published as Duke Math. J. 171 (2022), no. 4, 885-956 · 54 pages, 23 figures; v2: accepted version
arxiv created 2021/04/13 · openalex publication_date 2022/02/23 · arxiv updated 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer homology and contact geometry. It uses open books; the contact invariants we defined in the instanton Floer setting; a bypass exact triangle in sutured instanton homology, proven here; and Kronheimer and Mrowka's spectral sequence relating Khovanov homology with singular instanton knot homology. As a byproduct, we also strengthen a result of Kronheimer and Mrowka on SU(2) representations of the knot group.