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Kontsevich integral for knots and Vassiliev invariants

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arxiv 1112.5406 v3 pith:FTZVMWLO submitted 2011-12-22 hep-th math.COmath.GT

Petr Dunin-Barkowski , Alexey Sleptsov , Andrey Smirnov This is my paper · ORCID
classification hep-thmath.COmath.GT
keywords integralinvariantskontsevichvassilievgaugeresultstheoryapproach
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We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal gauge considerations which lead to representation of Vassiliev invariants in terms of arrow diagrams. Explicit examples and computational results are presented.

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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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