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.
Framed knot contact homology
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in $S^3$ and can be generalized to knots in arbitrary manifolds, distinguishes the unknot and can distinguish mutants. It contains the Alexander polynomial and naturally produces a two-variable polynomial knot invariant which is related to the $A$-polynomial.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
A cord algebra is defined for tori surrounding knots and identified with the knot cord algebra, indirectly relating it to Legendrian contact homology of the unit conormal bundle.
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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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A cord algebra for tori in three-space
A cord algebra is defined for tori surrounding knots and identified with the knot cord algebra, indirectly relating it to Legendrian contact homology of the unit conormal bundle.