Year: 2025
Type: article
Abstract: We exhibit infinitely many ribbon knots, each of which bounds infinitely many pairwise nonisotopic 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 up to isotopy. Precisely, we show that each generalized square knot bounds infinitely many pairwise nonisotopic fibered, homotopy‐ribbon disks, all of whose exteriors are diffeomorphic. When , we prove further that infinitely many of these disks are also ribbon; whether the disks are always ribbon is an open problem.
Source: Journal of Topology
DOI: 10.1112/topo.70047
Authors: Jeffrey Meier, Alexander Zupan
Institutions: Western Washington University, University of Nebraska–Lincoln
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
Funder: National Science Foundation
OpenAlex ID: W4416715467