On the functoriality of Khovanov homology
Dorra Hamza
TL;DR
This paper reviews Blanchet's oriented Khovanov homology model, clarifies its functoriality, and discusses extensions to cobordisms with singularities, advancing the mathematical understanding of link invariants.
Contribution
It provides a detailed exposition of Blanchet's oriented Khovanov homology and establishes its strict functoriality, resolving previous sign ambiguities.
Findings
Established strict functoriality for the oriented model
Resolved sign ambiguity in functoriality
Outlined extension to cobordisms with singularities
Abstract
We provide an overview of Blanchet's oriented model of Khovanov homology, which resolves the sign ambiguity in functoriality. We give a detailed and self-contained exposition of the construction. We establish strict functoriality for the oriented model and briefly outline its extension to cobordisms with singularities recently studied by Scott Carter, Benjamin Cooper, Mikhail Khovanov and Vyacheslav Krushkal.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Operator Algebra Research