Kontsevich integral for knots and Vassiliev invariants

Details Kontsevich integral for knots and Vassiliev invariants Kontsevich integral for knots and Vassiliev invariants

2011-12-22

arxiv.org/abs/1112.5406v3

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 17 figures

Scientific paper

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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