Matrix factorizations and double line in $\mathfrak{sl}_n$ quantum link invariant

Details Matrix factorizations and double line in $\mathfrak{sl}_n$ quantum link invariant Matrix factorizations and double line in $\mathfrak{sl}_n$ quantum link invariant

2007-03-27

arxiv.org/abs/math/0703779v2

Mathematics

Geometric Topology

17 pages

Scientific paper

This article gives matrix factorizations for the trivalent diagrams and double line appearing in $\mathfrak{sl}_n$ quantum link invariant. These matrix factorizations reconstruct Khovanov-Rozansky homology. And we show that the Euler characteristic of the matrix factorization for a double loop equals the quantum dimension of the representation $\land^2 V$ of $U_q (\mathfrak{sl}_n)$ in Section \ref{sec3.3}.

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