Characterisation of homotopy ribbon discs

Conway, Anthony; Powell, Mark

Abstract

Let Γ be either the infinite cyclic group Z or the Baumslag-Solitar group Zn Z[ 1 2 ]. Let K be a slice knot admitting a slice disc D in the 4-ball whose exterior has fundamental group Γ. We classify the Γ-homotopy ribbon slice discs for K up to topological ambient isotopy rel. boundary. In the infinite cyclic case, there is a unique equivalence class of such slice discs. When Γ is the Baumslag-Solitar group, there are at most two equivalence classes of Γhomotopy ribbon discs, and at most one such slice disc for each lagrangian of the Blanchfield pairing of K.

Citation

Conway, A., & Powell, M. (2021). Characterisation of homotopy ribbon discs. Advances in Mathematics, 391, Article 107960. https://doi.org/10.1016/j.aim.2021.107960

• Journal Article Type: Article
• Acceptance Date: Jul 9, 2021
• Online Publication Date: Aug 14, 2021
• Publication Date: Nov 19, 2021
• Deposit Date: Jul 20, 2021
• Publicly Available Date: Aug 14, 2022
• Journal: Advances in Mathematics
• Print ISSN: 0001-8708
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 391
• Article Number: 107960
• DOI: https://doi.org/10.1016/j.aim.2021.107960
• Public URL: https://durham-repository.worktribe.com/output/1271762
• Related Public URLs: https://arxiv.org/abs/1902.05321