Computing Khovanov–Rozansky homology and defect fusion

Abstract

We compute the categorified $\mathfrak{s}\mathfrak{l}\left(N\right)$ link invariants as defined by Khovanov and Rozansky, for various links and values of $N$. This is made tractable by an algorithm for reducing tensor products of matrix factorizations to finite rank, which we implement in the computer algebra package Singular.