Ribbon concordance and fibered predecessors
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912623587491840 |
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| author | Baldwin, John A. Sivek, Steven |
| author_facet | Baldwin, John A. Sivek, Steven |
| contents | Given any knot K in the 3-sphere, we prove that there are only finitely many hyperbolic fibered knots which are ribbon concordant to K. It follows that every fibered knot in the 3-sphere has only finitely many hyperbolic predecessors under ribbon concordance. Our proof combines results about maps on Floer homology induced by ribbon cobordisms with a relationship between the knot Floer homology of a fibered knot and fixed points of its monodromy. We then use the same techniques in combination with results of Cornish and Kojima-McShane to prove an inequality relating the volumes of ribbon concordant hyperbolic fibered knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ribbon concordance and fibered predecessors Baldwin, John A. Sivek, Steven Geometric Topology Given any knot K in the 3-sphere, we prove that there are only finitely many hyperbolic fibered knots which are ribbon concordant to K. It follows that every fibered knot in the 3-sphere has only finitely many hyperbolic predecessors under ribbon concordance. Our proof combines results about maps on Floer homology induced by ribbon cobordisms with a relationship between the knot Floer homology of a fibered knot and fixed points of its monodromy. We then use the same techniques in combination with results of Cornish and Kojima-McShane to prove an inequality relating the volumes of ribbon concordant hyperbolic fibered knots. |
| title | Ribbon concordance and fibered predecessors |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2510.02214 |