The Combinatorial Gauss Diagram Formula for Kontsevich Integral
نویسنده
چکیده
In this paper, we shall give an explicit Gauss diagram formula for the Kontsevich integral of links up to degree four. This practical formula enables us to actually compute the Kontsevich integral in a combinatorial way.
منابع مشابه
Chord diagram invariants of tangles and graphs
The notion of a chord diagram emerged from Vassiliev's work Vas90], Vas92] (see also Gusarov Gus91], Gus94] and Bar-Natan BN91], BN95]). Slightly later, Kontsevich Kon93] deened an invariant of classical knots taking values in the algebra generated by formal linear combinations of chord diagrams modulo the four-term relation. This knot invariant establishes an isomorphism of a projective limit ...
متن کاملInvariants of plane curves and Gauss diagram formulas for the Kontsevich integral
In a previous paper, we derive the Gauss diagram formulas for the Kontsevich integral of links up to degree four. The formulas consist of two parts. One part depends on the signs of knot diagrams, while the other depends only on their projection to the plane. In this paper, we express the latter part in terms of Arnold’s invariants of plane curves J+, J− and St up to degree three.
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We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as a coloring of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.
متن کاملO ct 2 00 3 On Kontsevich Integral of torus knots ∗
We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.
متن کاملOn Kontsevich Integral of torus knots
We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.
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