Volume 22, issue 3 (2022)

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Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Holt Bodish

Algebraic & Geometric Topology 22 (2022) 1273–1285
Abstract

We use work of Lawson, Lipshitz and Sarkar as well as Wilson, Levine and Zemke to prove that there are prime knots — in fact, hyperbolic and prime satellite knots — with arbitrarily high Steenrod squares on their (reduced and unreduced) Khovanov homology.

Keywords
knot theory, Khovanov homology, Steenrod operations, homotopy type, ribbon concordance
Mathematical Subject Classification
Primary: 57K18
Secondary: 55P42, 57N70
References
Publication
Received: 4 August 2020
Revised: 21 January 2021
Accepted: 3 May 2021
Published: 25 August 2022
Authors
Holt Bodish
Department of Mathematics
University of Oregon
Eugene, OR
United States