A universal equivariant finite type knot invariant defined from configuration space integrals - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

A universal equivariant finite type knot invariant defined from configuration space integrals

Christine Lescop

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.
Fichier principal
Vignette du fichier
Bonnclasphal.pdf (595.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00831624 , version 1 (07-06-2013)

Identifiants

Citer

Christine Lescop. A universal equivariant finite type knot invariant defined from configuration space integrals. 2013. ⟨hal-00831624⟩

Collections

CNRS FOURIER INSMI
94 Consultations
41 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More