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