# On configuration space integrals for links

@inproceedings{Lescop2002OnCS, title={On configuration space integrals for links}, author={C. Lescop}, year={2002} }

We give an introductory survey on the universal Vassiliev in- variant called the perturbative series expansion of the Chern{Simons theory of links in euclidean space, and on its relation with the Kontsevich inte- gral. We also prove an original geometric property of the anomaly of Bott, Taubes, Altschuler, Freidel and D. Thurston, that allowed Poirier to prove that the Chern{Simons series and the Kontsevich integral coincide up to degree 6. AMS Classication 57M27; 57M25, 17B37, 81T18

## 10 Citations

A SURVEY OF BOTT–TAUBES INTEGRATION

- Mathematics
- 2005

It is well-known that certain combinations of configuration space integrals defined by Bott and Taubes [11] produce cohomology classes of spaces of knots. The literature surrounding this important…

On the homology of the space of knots

- Mathematics
- 2005

Consider the space of long knots in R , Kn;1 . This is the space of knots as studied by V Vassiliev. Based on previous work (Budney [7], Cohen, Lada and May [12]), it follows that the rational…

Perturbative expansion of Chern-Simons theory

- Mathematics
- 2005

An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of…

Framing and the Self-Linking Integral

- Mathematics
- 2002

The Gauss self-linking integral of an unframed knot is not a knot invariant, but it can be turned into an invariant by adding a correction term which requires adding extra structure to the knot. We…

An Invariant of Embeddings of 3-Manifolds in 6-Manifolds and Milnor's Triple Linking Number

- Mathematics
- 2008

We give a simple axiomatic definition of a rational- valued invariant σ(W, V, e )o ftriples (W, V, e), where W ⊃ V are smooth oriented closed manifolds of dimensions 6 and 3, and e is a second…

The non-Abelian Chern-Simons path integral on $M=\Sigma \times S^1$ in the torus gauge: a review

- Physics, Mathematics
- 2018

In the present paper we review the main results of a series of recent papers on the non-Abelian Chern-Simons path integral on $M=\Sigma \times S^1$ in the so-called "torus gauge". More precisely, we…

Finite Type Invariants

- Mathematics
- 2004

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

BIBLIOGRAPHY OF VASSILIEV INVARIANTS

- Mathematics
- 2013

1. List of Additions 2 2. Electronic Addresses 5 3. Acknowledgement 12 4. References 12 4.1. References beginning with A 12 4.2. References beginning with B 13 4.3. References beginning with C 15…

De l'optimisation dans les réseaux

- Computer Science, Philosophy
- 2012

Ce memoire d'habilitation a diriger des recherches traite de problemes d'optimisation dans les reseaux, dont la modelisation et la resolution reposent sur les outils de la recherche operationnelle.…

Finite Type Invariants

- 2004

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

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We refine a Le and Murakami uniqueness theorem for the Kontsevich Integral in order to specify the relationship between the two (possibly equal) main universal link invariants: the Kontsevich…