Abstract We define a knot to be ₀ γ 0 - sharp if its Seifert genus is detected by the concordance invariant ₀ γ 0, which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of ₀ γ 0 -sharp fibered knots is ribbon exactly when it is of the form K \# -K K # - K. Consequently, either iterated cables of tight fibered knots are linearly independent in the smooth concordance group, or the slice–ribbon conjecture fails.
Hom et al. (Thu,) studied this question.
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