Knot Floer homology and Seifert surfaces

2007/02/28 by Andras Juhasz · 5 citations
Mathematics · #Advanced Combinatorial Mathematics #Alexander polynomial #Algebraic Geometry and Number Theory #Disjoint sets #Fibered knot #Floer homology #Geometric and Algebraic Topology #Knot (papermaking) #Knot complement #Seifert surface #math.GT #msc:57M27 #msc:57R58

paper · pdf · doi:10.2140/agt.2008.8.603

published in Algebraic & Geometric Topology 8(1), 603-608 (Mathematical Sciences Publishers) · 4 pages, n=0 case corrected

arxiv created 2007/03/05 · openalex publication_date 2008/05/12 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Let K be a knot in S 3 of genus g and let n > 0: We show that if rk 1 HFK .K; g/ < 2 nC1 (where 1 HFK denotes knot Floer homology), in particular if K is an alternating knot such that the leading coefficient a g of its Alexander polynomial satisfies ja g j < 2 nC1 ; then K has at most n pairwise disjoint nonisotopic genus g Seifert surfaces.

Citations

• Foliations and the topology of 3-manifolds
• Holomorphic disks and knot invariants
• Heegaard Floer homology and alternating knots
• Floer homology and surface decompositions
• Knot Floer homology detects fibred knots