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

By Hao Wu. 2009

88 citations recorded by the source corpus.

Fix an integer N>1. 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 in arXiv:math/0401268. The homology of this chain complex decategorifies to the Reshetikhin-Turaev sl(N) polynomial of links colored by exterior powers of the defining representation.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0574b27f1b0096d165fa8746ebf5b09ade4caf03

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Citations in the corpus

Deformations of colored sl(N) link homologies via foams (2015, result): “This was later extended by Wu [43] and Yonezawa [44] to a categorified invariant of links whose components are colored by fundamental representations VkCN of slN for 0 k N .”
Homological algebra of knots and BPS states (2011, background): “Let us denote by Hg,R a homology theory of knots and links colored by a representation R of the Lie algebra g. Many such homology theories can be constructed using categories of matrix factorizations [33, 34, 35, 36, 37, 38, 39, 40]. In this approach, one of the main ingredients is a polynomial func”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “For general sln, matrix factorizations become the primary computation tool [77, 76, 75], and the only way to evaluate a closed foam is through the mysterious Kapustin-Li formula [51, 23].”