The knot Floer complex and the smooth concordance group

2011/11/28 by Jennifer Hom · 1 citation
Computer Science · Mathematics · Medicine · #Combinatorics #Composite material #Concordance #Floer homology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Internal medicine #Knot (papermaking) #Mathematics #Medicine #Pure mathematics #math.GT #msc:57M25 #msc:57R58 #semigroups and automata theory

paper · pdf · doi:10.4171/cmh/326

published as Commentarii Mathematici Helvetici 89 (2014) 537-570 · 25 pages, 5 figures

arxiv created 2011/11/28 · openalex publication_date 2014/09/11 · arxiv updated 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant ε . As an application, we show that an infinite family of topologically slice knots are independent in the smooth concordance group.

Citations

• The topology of four-dimensional manifolds
• Floer homology and knot complements
• Bordered Heegaard Floer homology
• Holomorphic disks and knot invariants
• Legendrian knots, transverse knots and combinatorial Floer homology
• On knot Floer homology and cabling II

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