On configuration space integrals for links

@inproceedings{Lescop2002OnCS,
  title={On configuration space integrals for links},
  author={C. Lescop},
  year={2002}
}
  • C. Lescop
  • Published 21 September 2002
  • Mathematics
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 
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References

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The perturbative expression of Chern-Simons theory for links in Euclidean 3-space is a linear combination of integrals on configuration spaces. This has successively been studied by Guadagnini,Expand
The Configuration space integral for links and tangles in R^3
The perturbative expression of Chern-Simons theory for links in Euclidean 3-space is a linear combination of integrals on configuration spaces. This has successively been studied by Guadagnini,Expand
The universal Vassiliev-Kontsevich invariant for framed oriented links
We give a generalization of the Reshetikhin-Turaev functor for tangles to get a combinatorial formula for the Kontsevich integral for framed oriented links. The rationality of the Kontsevich integralExpand
ABOUT THE UNIQUENESS OF THE KONTSEVICH INTEGRAL
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 Vassiliev link invariants: theExpand
Vassiliev Knot Invariants and Chern-Simons Perturbation Theory to All Orders
Abstract:At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants.Expand
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It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory,Expand
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We study the perturbation theory for three dimensional Chern--Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, theExpand
Perturbative 3-manifold invariants by cut-and-paste topology
Author(s): Kuperberg, Greg; Thurston, Dylan P. | Abstract: We give a purely topological definition of the perturbative quantum invariants of links and 3-manifolds associated with Chern-Simons fieldExpand
PERTURBATIVE CHERN-SIMONS THEORY
We present the perturbation theory of the Chern-Simons gauge field theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get aExpand
About the uniqueness and the denominators of the Kontsevich Integral
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 KontsevichExpand
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