gl(2) foams and the Khovanov homotopy type

Abstract

The Blanchet link homology theory is an oriented model of Khovanov homology, functorial over the integers with respect to link cobordisms. We formulate a stable homotopy refinement of the Blanchet theory, based on a comparison of the Blanchet and Khovanov chain complexes associated to link diagrams. The construction of the stable homotopy type relies on the signed Burnside category approach of Sarkar-Scaduto-Stoffregen.

arXiv comment23 pages

References in corpus (14)

• Khovanov's homology for tangles and cobordisms
• An invariant of link cobordisms from Khovanov homology
• A Khovanov stable homotopy type
• Super $q$-Howe duality and web categories
• Deformations of colored sl(N) link homologies via foams
• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• Khovanov homotopy type, Burnside category, and products
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Field theories, stable homotopy theory and Khovanov homology
• A closed formula for the evaluation of ${\mathfrak{sl}}_N$-foams
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Fixing the functoriality of Khovanov homology: a simple approach
• An odd Khovanov homotopy type
• Extremal weight projectors II

Cited by in corpus (1)

• Homotopy functoriality for Khovanov spectra