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<p>We define a knot to be <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>γ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-<i>sharp</i> if its Seifert genus is detected by the concordance invariant <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>γ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>γ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-sharp fibered knots is ribbon exactly when it is of the form <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(K \mathbin {\#} -K\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>#</mo> <mo>-</mo> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation>. Consequently, either iterated cables of tight fibered knots are linearly independent in the smooth concordance group, or the slice–ribbon conjecture fails.</p>

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Ribbon knots and iterated cables of fibered knots

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月18日

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  • Jennifer Hom,
  • JungHwan Park

摘要

We define a knot to be \(\gamma _0\) γ 0 -sharp if its Seifert genus is detected by the concordance invariant \(\gamma _0\) γ 0 , which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of \(\gamma _0\) γ 0 -sharp fibered knots is ribbon exactly when it is of the form \(K \mathbin {\#} -K\) K # - K . Consequently, either iterated cables of tight fibered knots are linearly independent in the smooth concordance group, or the slice–ribbon conjecture fails.