Displaying similar documents to “An invariant of link cobordisms from Khovanov homology.”

A colored 𝔰𝔩(N) homology for links in S³

Hao Wu

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Fix an integer N ≥ 2. To each diagram of a link colored by 1,...,N we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every component of the link is colored by 1, this chain complex is isomorphic to the chain complex defined by Khovanov and Rozansky. The homology of this chain complex decategorifies to the Reshetikhin-Turaev 𝔰𝔩(N) polynomial of links colored by exterior powers...

Khovanov homology, its definitions and ramifications

Oleg Viro (2004)

Fundamenta Mathematicae

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Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these...

An infinite torus braid yields a categorified Jones-Wenzl projector

Lev Rozansky (2014)

Fundamenta Mathematicae

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A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.