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.
Invariants of links of Conway type
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial invariants of Conway and Jones. These invariants have one striking common feature. If L+, L- and L0 are diagrams of oriented links which are identical, except near one crossing point (as in Conway or Jones polynomials), then an invariant w(L) has the property: w(L+) is uniquely determined by w(L-) and w(L0), and also w(L-) is uniquely determined by w(L+) and w(L0). To formalize this property we introduce a concept of a Conway algebra and quasi Conway algebra. The paper is now almost 32 years old and it contains the PT contribution to HOMFLYPT polynomial. We believe it should be available in arXiv.
verdicts
UNVERDICTED 3representative citing papers
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.
citing papers explorer
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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.