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Dunin-Barkowski, P.; Sleptsov, A.; Smirnov, A.

Kontsevich integral for knots and Vassiliev invariants. (English) Zbl 1272.81179

Int. J. Mod. Phys. A 28, No. 17, Article ID 1330025, 38 p. (2013).
Summary: 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.

Cited in 13 Documents

MSC:

81T45 Topological field theories in quantum mechanics
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
58J28 Eta-invariants, Chern-Simons invariants

Keywords:

Kontsevich integral; Vassiliev invariants; gauge theory; trivalent diagrams; Chern-Simons theory; Wilson loops; knots
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References:

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