2023/10/26 by Jeffery L. Meier, Meier, Jeffrey, Alexander Zupan +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Algebraic Geometry and Number Theory #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2310.17564
openalex publication_date 2023/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exhibit infinitely many ribbon knots, each of which bounds infinitely many pairwise non-isotopic ribbon disks whose exteriors are diffeomorphic. This family provides a positive answer to a stronger version of an old question of Hitt and Sumners. The examples arise from our main result: a classification of fibered, homotopy-ribbon disks for each generalized square knot Tp,q# Tp,q up to isotopy. Precisely, we show that each generalized square knot bounds infinitely many pairwise non-isotopic fibered, homotopy-ribbon disks, all of whose exteriors are diffeomorphic. When q=2, we prove further that infinitely many of these disks are also ribbon; whether the disks are always ribbon is an open problem.