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Unknotting number and cabling

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arxiv 2206.04196 v1 pith:J3JSEJWM submitted 2022-06-08 math.GT

Jennifer Hom , Tye Lidman , JungHwan Park This is my paper · ORCID
classification math.GT
keywords numberunknottingknotscablefloerhomologyknotterms
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The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unknotting number of cable knots and iterated cable knots purely in terms of the winding number of the pattern. The proof uses Alishahi-Eftekhary's bounds on unknotting number from knot Floer homology together with Hanselman-Watson's computation of the knot Floer homology of cables in terms of immersed curves in the punctured torus.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ribbon concordance and cabling

    math.GT 2026-08 conditional novelty 7.0 of 10

    A new height invariant from immersed-curve knot Floer homology gives rigidity results for knots that ribbon-concord to cable knots.

  2. Naturality in real Heegaard Floer theory

    math.GT 2026-07 conditional novelty 7.0 of 10

    Real Heegaard Floer homology becomes a natural functor on based real 3-manifolds, with an equivariant mapping class group action and a new involutive variant.

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