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We define a second Steenrod square for virtual links, which is stronger thanKhovanov homology for virtual links, toward constructingKhovanov-Lipshitz-Sarkar stable homotopy type for virtual links. This inducesthe first meaningful nontrivial example of the second Steenrod square operatoron the Khovanov homology for links in a 3-manifold other than the 3-sphere.

Steenrod square for virtual links toward Khovanov-Lipshitz-Sarkar stable homotopy type for virtual links