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.
Planar decomposition of the HOMFLY polynomial for bipartite knots and links
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Authors propose shaded A-polynomials A_a(ℓ_b, m_c) for SU(N) via CG chords from huge representations of U_q(su_N) in the classical limit, with examples for knots 3_1, 4_1, 5_1 in su_3.
A modified Goeritz matrix is defined for bipartite link diagrams that reduces HOMFLY-PT computation for any N to matrix algebra.
Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.
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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Shading A-polynomials via huge representations of $U_q(\mathfrak{su}_N)$
Authors propose shaded A-polynomials A_a(ℓ_b, m_c) for SU(N) via CG chords from huge representations of U_q(su_N) in the classical limit, with examples for knots 3_1, 4_1, 5_1 in su_3.
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Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials
A modified Goeritz matrix is defined for bipartite link diagrams that reduces HOMFLY-PT computation for any N to matrix algebra.
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Two roles of Alexander in two Kashaev phases
Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.
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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.