The authors construct positive decompositions of fundamental HOMFLY polynomials in variables φ, φ̄, D for arbitrary knots, not just bipartite ones, and give a criterion to detect when such a decomposition conceals a bipartite realization.
A computation in Khovanov-Rozansky Homology
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abstract
We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl_3-homology.
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Bipartite expansion beyond biparticity
The authors construct positive decompositions of fundamental HOMFLY polynomials in variables φ, φ̄, D for arbitrary knots, not just bipartite ones, and give a criterion to detect when such a decomposition conceals a bipartite realization.