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Characterisation of homotopy ribbon discs

Conway, Anthony; Powell, Mark

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Authors

Anthony Conway

Mark Powell



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
Related Public URLs https://arxiv.org/abs/1902.05321

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