Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Bodish, Holt

doi:10.2140/agt.2022.22.1273

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Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Holt Bodish

Algebraic & Geometric Topology 22 (2022) 1273–1285

DOI: 10.2140/agt.2022.22.1273

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.

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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

Volume 22, issue 3 (2022)