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More concordance homomorphisms from knot Floer homology

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arxiv 1902.03333 v2 pith:QKJ42JAU submitted 2019-02-09 math.GT

Irving Dai , Jennifer Hom , Matthew Stoffregen , Linh Truong This is my paper · ORCID
classification math.GT
keywords concordancehomomorphismsfloerknothomologyapplicationsclassescoming
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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.

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  1. L-space satellite operators and knot Floer homology

    math.GT 2024-12 conditional novelty 8.0 of 10

    For satellites whose pattern link is a 2-component L-space link, the full knot Floer complex is computed from the companion's complex and the pattern's Alexander polynomials.

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