2025/10/02 by John A. Baldwin, Baldwin, John A., Steven Sivek +1
Computer Science · #FOS: Mathematics #Geometric Topology (math.GT) #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2510.02214
openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.