Doubly slice knots and metabelian obstructions

Orson, P. and Powell, M. (2022) Doubly slice knots and metabelian obstructions. Journal of Topology and Analysis, 14(4), pp. 847-873. (doi: 10.1142/S1793525321500229)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Dr Mark
• Authors: Orson, P., and Powell, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Topology and Analysis
• Publisher: World Scientific Publishing
• ISSN: 1793-5253
• ISSN (Online): 1793-7167
• Published Online: 06 February 2021
• Copyright Holders: Copyright © 2022 World Scientific Publishing
• First Published: First published in Journal of Topology and Analysis 14(4): 847-873
• Publisher Policy: Reproduced in accordance with the publisher copyright policy