A lower bound for the doubly slice genus from signatures

Orson, P. and Powell, M. (2021) A lower bound for the doubly slice genus from signatures. New York Journal of Mathematics, 27, pp. 379-392.

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The doubly slice genus of a knot in the 3-sphere is the minimal genus among unknotted orientable surfaces in the 4-sphere for which the knot arises as a cross-section. We use the classical signature function of the knot to give a new lower bound for the doubly slice genus. We combine this with an upper bound due to C. McDonald to prove that for every nonnegative integer N there is a knot where the difference between the slice and doubly slice genus is exactly N, refining a result of W. Chen which says this difference can be arbitrarily large.

Item Type:Articles (Other)
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:New York Journal of Mathematics
Publisher:University at Albany
ISSN (Online):1076-9803
Copyright Holders:Copyright © The Author(s) 2021
First Published:First published in New York Journal of Mathematics 27: 379-392
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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