2006/07/31 by Yi Ni · 8 citations
Mathematics · Medicine · #Alexander polynomial #Botulinum Toxin and Related Neurological Disorders #Combinatorics #Conjecture #Corollary #Fibered knot #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot complement #Knot invariant #Knot theory #Mathematics #Pure mathematics #Symplectic geometry #math.GT #msc:57M27 #msc:57R30 #msc:57R58
paper · pdf · doi:10.1007/s00222-007-0075-9
version 4: incorporates referee's suggestions, to appear in Inventiones Mathematicae
arxiv created 2007/09/15 · openalex publication_date 2007/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S3. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if K is a knot in a closed 3--manifold Y, Y-K is irreducible, and HFK(Y,K) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsváth--Szabó, Ghiggini and the author. A corollary is that if a knot in S3 admits a lens space surgery, then the knot is fibred.