# The Kontsevich Integral

@article{Chmutov2001TheKI, title={The Kontsevich Integral}, author={Sergei Chmutov and Sergei Duzhin}, journal={Acta Applicandae Mathematica}, year={2001}, volume={66}, pages={155-190} }

The paper contains a detailed exposition of the construction and properties of the Kontsevich integral invariant, crucial in the study of Vassiliev knot invariants.

## 51 Citations

### The Generating Functional of the Kontsevich Integral and its Derivation as a Holonomy

- Mathematics
- 2012

We introduce an algebra bundle of chord diagrams over the configuration space of N points in the complex plane on which we put the Knizhnik-Zamolodchikov connection. For that particular connection,…

### Knot invariants and configuration space integrals

- Mathematics
- 2005

After a short presentation of the theory of Vassiliev knot invariants, we shall introduce a universal finite type invariant for knots in the ambient space. This invariant is often called the…

### A Stringy Generalization of the Kontsevich Integral

- Mathematics
- 2012

We introduce a "minimal" Kontsevich integral that generates the original Kontsevich integral while at the same time producing ribbons whose boundaries are the braids on which the minimal Kontsevich…

### KONTSEVICH INTEGRAL FOR KNOTS AND VASSILIEV INVARIANTS

- Mathematics
- 2013

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…

### On the Kontsevich integral of Brunnian links

- Mathematics
- 2006

The purpose of the paper is twofold. First, we give a short proof using the Kontsevich integral for the fact that the restriction of an invariant of degree 2n to (n+1)-component Brunnian links can be…

### Finite Type Invariants

- Mathematics
- 2004

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics.

### Knot Theory With The Lorentz Group

- Mathematics
- 2003

We analyse the perturbative expansion of the knot invariants defined from the unitary representations of the Quantum Lorentz Group in two different ways, namely using the Kontsevich Integral and…

### On the Kontsevich integral for knotted trivalent graphs

- Mathematics
- 2010

We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami…

### On the Existence of Finite Type Link Homotopy Invariants

- Mathematics
- 2000

We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there…

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Kontserich a donne recemment une construction explicite des inrariants des noeuds introduits par Vassilier. Nous proposons une construction combinatoire utilisant une projection plane, et des calculs…