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

2020/01/21 by Louis H. Kauffman, Kauffman, Louis H., Eiji Ogasa +1
Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2001.07789

openalex publication_date 2020/01/21 · openalex created_date 2020/01/30 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Bordered Heegaard Floer homology
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds

Related

• Computations of the Lipshitz-Sarkar Steenrod Square on Khovanov Homology
• Khovanov-Lipshitz-Sarkar homotopy type for links in thickened higher genus surfaces
• On Steenrod squares for even and odd Khovanov homology
• Khovanov homotopy calculations using flow category calculus
• Two second Steenrod squares for odd Khovanov homology