Ribbon knots and iterated cables of fibered knots

Jennifer Hom; JungHwan Park

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arXiv · 2507.20455

Ribbon knots and iterated cables of fibered knots

Jennifer Hom·JungHwan Park

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Abstract

We define a knot to be $\gamma_0$-sharp if its Seifert genus is detected by the concordance invariant $\gamma_0$, which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of $\gamma_0$-sharp fibered knots is ribbon exactly when it is of the form $K \mathbin{\#} -K$. Consequently, either iterated cables of tight fibered knots are linearly independent in the smooth concordance group, or the slice--ribbon conjecture fails.

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Jennifer Hom, JungHwan Park. 2025-07-28. Ribbon knots and iterated cables of fibered knots. https://arxiv.org/abs/2507.20455

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