Two second Steenrod squares for odd Khovanov homology
Tom 271 / 2025
Fundamenta Mathematicae 271 (2025), 29-69
MSC: Primary 58K18; Secondary 58K10
DOI: 10.4064/fm240612-26-8
Opublikowany online: 8 October 2025
Streszczenie
Recently, Sarkar–Scaduto–Stoffregen constructed a stable homotopy type for odd Khovanov homology, hence obtaining an action of the Steenrod algebra on Khovanov homology with $\mathbb Z/2\mathbb Z$ coefficients. Motivated by their construction we propose a way to compute the second Steenrod square. Our construction is not unique, but we can show it to be a link invariant which gives rise to a refinement of the Rasmussen $s$-invariant with $\mathbb Z/2\mathbb Z$ coefficients. We expect it to be related to the second Steenrod square arising from the Sarkar–Scaduto–Stoffregen construction.
