Khovanov-Rozansky invariants are recast as a bicomplex of local operators D and conjugations χ^(±), with nilpotency on closed diagrams allowing reductions that simplify the hypercube construction.
Introduction to Khovanov homologies I. Unreduced Jones superpolynomial
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abstract
An elementary introduction to Khovanov construction of superpolynomials. Despite its technical complexity, this method remains the only source of a definition of superpolynomials from the first principles and therefore is important for development and testing of alternative approaches. In this first part of the review series we concentrate on the most transparent and unambiguous part of the story: the unreduced Jones superpolynomials in the fundamental representation and consider the 2-strand braids as the main example. Already for the 5_1 knot the unreduced superpolynomial contains more items than the ordinary Jones.
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hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Shows that the Kauffman-Khovanov 2²-hypercube reduces to the bipartite 3-hypercube for N=2, confirming consistency of the reduction for bipartite links.
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Reductions in Khovanov-Rozansky operator formalism
Khovanov-Rozansky invariants are recast as a bicomplex of local operators D and conjugations χ^(±), with nilpotency on closed diagrams allowing reductions that simplify the hypercube construction.
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Khovanov complexes for bipartite links
Shows that the Kauffman-Khovanov 2²-hypercube reduces to the bipartite 3-hypercube for N=2, confirming consistency of the reduction for bipartite links.