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Link Floer homology detects the Thurston norm

2006/04/16 by Yi Ni · 68 citations
Mathematics · Medicine · #Algebra over a field #Amino acid #Botulinum Toxin and Related Neurological Disorders #Cellular homology #Combinatorics #Floer homology #Genetics #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Law #Link (geometry) #Mathematics #Morse homology #Norm (philosophy) #Pure mathematics #Symplectic geometry #math.GT #msc:57M27 #msc:57R30 #msc:57R58

paper · pdf · doi:10.2140/gt.2009.13.2991

published in Geometry & Topology 13(5), 2991-3019 (Mathematical Sciences Publishers) · 25 pages, 1 figure

arxiv created 2006/04/16 · openalex publication_date 2009/09/18 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that, for a link L in a rational homology 3–sphere, the link Floer homology detects the Thurston norm of its complement. This result has been proved by Ozsváth and Szabó for links in S3. As an ingredient of the proof, we show that knot Floer homology detects the genus of null-homologous links in rational homology spheres, which is a generalization of an earlier result of the author. Our argument uses the techniques due to Ozsváth and Szabó, Hedden and the author.

Citations