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)

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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
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 (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

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