A colored sl(N)-homology for links in S^3

Details A colored sl(N)-homology for links in S^3 A colored sl(N)-homology for links in S^3

2009-07-03

arxiv.org/abs/0907.0695v5

Mathematics

Geometric Topology

200 pages, 117 figures. Fifth version: added a proof that the colored $\mathfrak{sl}(N)$-homology categorifies the correspondi

Scientific paper

Fix an integer $N\geq 2$. 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. We call the homology of this chain complex the colored $\mathfrak{sl}(N)$-homology and prove that it decategorifies to the Reshetikhin-Turaev $\mathfrak{sl}(N)$-polynomial of links colored by exterior powers of the defining representation.

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