More concordance homomorphisms from knot Floer homology

Abstract

We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes of knot Floer complexes over the ring $\mathbb{F}[U,V]/(UV=0)$. We compare our invariants to other concordance homomorphisms coming from knot Floer homology, and discuss applications to topologically slice knots, concordance genus, and concordance unknotting number.

arXiv comment50 pages, 6 figures v2: Included a 2 page erratum pointing out an error in a lemma, along with a reference to a revised and correct version of the lemma. The main results of the paper are unaffected

References in corpus (9)

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• Holomorphic disks and genus bounds
• Concordance homomorphisms from knot Floer homology
• The knot Floer complex and the smooth concordance group
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Cited by in corpus (9)

• Cabling in terms of immersed curves
• Linear independence of rationally slice knots
• A survey of the homology cobordism group
• Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology
• Branched covers bounding rational homology balls
• Categorical lifting of the Jones polynomial: a survey
• A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence
• Twist positivity, L-space knots, and concordance
• Computation of the knot Floer complex of knots of thickness one