On Steenrod squares for even and odd Khovanov homology

2025/09/03 by Advika Rajapakse, Rajapakse, Advika · 1 citation
Mathematics · #55P42 #57K18 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.03396

openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an arbitrary link L ⊂ S³ , Sarkar-Scaduto-Stoffregen construct a family of spatial refinements of even and odd Khovanov homology. We give a computation of Sq² on these spaces, determining their stable homotopy types for all knots K up to 11 crossings. We also prove that the Steenrod squares Sq₀² , Sq₁² defined by Schütz do arise as Steenrod squares on these spaces.

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