On an integral version of the Rasmussen invariant

Schuetz, Dirk

Abstract

We define a Rasmussen s-invariant over the coefficient ring Z and show how it is related to the s-invariants defined over a field. A lower bound for the slice genus of a knot arising from it is obtained, and we give examples of knots for which this lower bound is better than all lower bounds coming from the s-invariants over fields. We also compare it to the Lipshitz–Sarkar refinement related to the first Steenrod square.

Citation

Schuetz, D. (2025). On an integral version of the Rasmussen invariant. Michigan Mathematical Journal, 75(1), 65-88. https://doi.org/10.1307/mmj/20226211

• Journal Article Type: Article
• Acceptance Date: Sep 30, 2022
• Online Publication Date: Dec 12, 2023
• Publication Date: 2025-03
• Deposit Date: Oct 4, 2022
• Journal: Michigan Mathematical Journal
• Print ISSN: 0026-2285
• Electronic ISSN: 1945-2365
• Publisher: Department of Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 75
• Issue: 1
• Pages: 65-88
• DOI: https://doi.org/10.1307/mmj/20226211
• Public URL: https://durham-repository.worktribe.com/output/1190350