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.

Abstract

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)
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Professor 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: 1076-9803
• 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