Concordance homomorphisms from knot Floer homology

2014/07/31 by Peter S. Ozsváth, Peter Ozsvath, András I. Stipsicz +3 · 189 citations
Mathematics · Medicine · #Bioinformatics #Botulinum Toxin and Related Neurological Disorders #Combinatorics #Concordance #Discrete mathematics #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot invariant #Knot theory #Mathematics #Pure mathematics #math.GT #msc:57M25 #msc:57R58

paper · pdf · doi:10.1016/j.aim.2017.05.017

published in Advances in Mathematics 315, 366-426 (Elsevier BV) · Minor revision, corrected typos and added explanation to Chapter 8

arxiv created 2017/06/13 · openalex publication_date 2017/06/13 · arxiv updated 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We modify the construction of knot Floer homology to produce a one-parameter family of homologies for knots in the three-sphere. These invariants can be used to give homomorphisms from the smooth concordance group to the integers, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.

Citations

• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds

Cited by

• An involutive upsilon knot invariant
• New Heegaard Floer slice genus and clasp number bounds
• On the fractional Dehn twist coefficients of branched coverings
• An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology
• Every negative amphichiral knot is rationally slice
• Annular link invariants from the Sarkar-Seed-Szabó spectral sequence
• Skein exact triangles in knot Floer homology
• Nonorientable surfaces bounded by knots: a geography problem
• Deformations of lattice cohomology and the upsilon invariant
• The bridge index and the braid index for twist positive knots
• Ribbon knots and iterated cables of fibered knots
• A note on the concordance invariants epsilon and upsilon
• A family of concordance homomorphisms from Khovanov homology
• A cabling formula for ν⁺ invariant
• Surgery exact triangles in involutive Heegaard Floer homology
• A Floer homology invariant for 3-orbifolds via bordered Floer theory
• On rational sliceness of Miyazaki's fibered, −amphicheiral knots
• Signature and concordance of virtual knots
• Branched covers bounding rational homology balls
• Rational concordance of double twist knots

Related

• Homology concordance and knot Floer homology
• Unoriented knot Floer homology and the unoriented four-ball genus
• A concordance invariant from the Floer homology of +/- 1 surgeries
• A family of concordance homomorphisms from Khovanov homology
• A note on knot concordance and involutive knot Floer homology