Doubly slice knots and metabelian obstructions

Orson, Patrick; Powell, Mark

doi:10.1142/s1793525321500229

Doubly slice knots and metabelian obstructions

Orson, Patrick; Powell, Mark

Authors

Patrick Orson

Mark Powell

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
Related Public URLs	https://arxiv.org/abs/1909.08127