Ribbon concordance and fibered predecessors

John A. Baldwin; Steven Sivek

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arXiv · 2510.02214

Ribbon concordance and fibered predecessors

John A. Baldwin·Steven Sivek

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Abstract

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.

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BibTeX RIS

John A. Baldwin, Steven Sivek. 2025-10-02. Ribbon concordance and fibered predecessors. https://arxiv.org/abs/2510.02214

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