Doubly slice knots and metabelian obstructions

Orson, Patrick; Powell, Mark

Abstract

An n-dimensional knot Sn⊂Sn+2 is called doubly slice if it occurs as the cross section of some unknotted (n+1)-dimensional knot. For every n it is unknown which knots are doubly slice, and this remains one of the biggest unsolved problems in high-dimensional knot theory. For ℓ>1, we use signatures coming from L(2)-cohomology to develop new obstructions for (4ℓ−3)-dimensional knots with metabelian knot groups to be doubly slice. For each ℓ>1, we construct an infinite family of knots on which our obstructions are nonzero, but for which double sliceness is not obstructed by any previously known invariant.

Citation

Orson, P., & Powell, M. (2022). Doubly slice knots and metabelian obstructions. Journal of Topology and Analysis, 14(4), 847-873. https://doi.org/10.1142/s1793525321500229

• Journal Article Type: Article
• Acceptance Date: Sep 15, 2020
• Online Publication Date: Feb 6, 2021
• Publication Date: 2022-12
• Deposit Date: Dec 21, 2020
• Publicly Available Date: Feb 6, 2022
• Journal: Journal of Topology and Analysis
• Print ISSN: 1793-5253
• Electronic ISSN: 1793-7167
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 14
• Issue: 4
• Pages: 847-873
• DOI: https://doi.org/10.1142/s1793525321500229
• Public URL: https://durham-repository.worktribe.com/output/1255191
• Related Public URLs: https://arxiv.org/abs/1909.08127