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A New Point of View in the Theory of Knot and Link Invariants

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arxiv math/0104180 v4 pith:BB6NBYIG submitted 2001-04-18 math.QA hep-thmath-phmath.MP

classification math.QAhep-thmath-phmath.MP
keywords invariantspolynomialcoefficientsdescribequantum-groupstructuretermstheory
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Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to construct the new polynomials and we conjecture their general structure. This leads to new conjectures on the algebraic structure of the quantum-group polynomial invariants. We also describe the geometrical meaning of the coefficients in terms of the enumerative geometry of Riemann surfaces with boundaries in a certain Calabi-Yau threefold.

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  1. Construction of Lie algebra weight system kernel via Vogel algebra

    math.QA 2024-11 conditional novelty 6.0 of 10

    Using Vogel's Lambda algebra, the authors construct and explicitly list the first Jacobi diagrams in the kernel of the sl_n weight system, up to order 10 for primitive diagrams.

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