gl(2) foams and the Khovanov homotopy type
Vyacheslav Krushkal, Paul Wedrich
TL;DR
This paper develops a stable homotopy refinement of Blanchet's oriented link homology theory, connecting it to Khovanov homology through a novel categorical approach, enhancing the understanding of link invariants.
Contribution
It introduces a stable homotopy type for Blanchet's link homology, bridging it with Khovanov homology using the signed Burnside category framework.
Findings
Constructed a stable homotopy type for Blanchet's theory
Established a comparison between Blanchet and Khovanov complexes
Enhanced functoriality over integers for link cobordisms
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics