Ribbon knots and iterated cables of fibered knots
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911079439794176 |
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| author | Hom, Jennifer Park, JungHwan |
| author_facet | Hom, Jennifer Park, JungHwan |
| contents | We define a knot to be $γ_0$-sharp if its Seifert genus is detected by the concordance invariant $γ_0$, which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of $γ_0$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ribbon knots and iterated cables of fibered knots Hom, Jennifer Park, JungHwan Geometric Topology We define a knot to be $γ_0$-sharp if its Seifert genus is detected by the concordance invariant $γ_0$, which arises from the immersed curve formalism in bordered Heegaard Floer homology. We show that a connected sum of $γ_0$-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. |
| title | Ribbon knots and iterated cables of fibered knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2507.20455 |