A universal equivariant finite type knot invariant defined from configuration space integrals
Résumé
In a previous article, we constructed an invariant Z for null-homologous knots in rational homology spheres, from equivariant intersections in configuration spaces. Here we present an equivalent definition of Z in terms of configuration space integrals, we prove that Z is multiplicative under connected sum, and we prove null Lagrangian-preserving surgery formulae for Z. Our formulae generalize similar formulae that are satisfied by the Kricker rational lift of the Kontsevich integral for null Borromean surgeries. They imply that Z is universal with respect to a natural filtration. According to results of Garoufalidis and Rozansky, they therefore imply that Z is equivalent to the Kricker lift of the Kontsevich integral for null-homologous knots with trivial Alexander polynomial in integral homology spheres.
Mots clés
- surgery formula
- Lagrangian-preserving surgery
- clasper calculus
- first Pontrjagin class
- beaded Jacobi diagrams
- perturbative expansion of Chern-Simons theory
- LMO invariant
- equivariant Blanchfield linking pairing
- rational lift of Kontsevich integral
- homology spheres
- finite type invariants of knots and 3-manifolds
- configuration space integrals
Domaines
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