Toward universality in degree 2 of the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant - Université de Bourgogne Accéder directement au contenu
Article Dans Une Revue International Journal of Mathematics Année : 2019

Toward universality in degree 2 of the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant

Résumé

In the setting of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries, there are two candidates to be universal invariants, defined, respectively, by Kricker and Lescop. In a previous paper, the second author defined maps between spaces of Jacobi diagrams. Injectivity for these maps would imply that Kricker and Lescop invariants are indeed universal invariants; this would prove in particular that these two invariants are equivalent. In the present paper, we investigate the injectivity status of these maps for degree 2 invariants, in the case of knots whose Blanchfield modules are direct sums of isomorphic Blanchfield modules of Q-dimension two. We prove that they are always injective except in one case, for which we determine explicitly the kernel.
Fichier principal
Vignette du fichier
Audoux_TowardUniversality.pdf (500.28 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02320375 , version 1 (22-01-2022)

Identifiants

Citer

Benjamin Audoux, Delphine Moussard. Toward universality in degree 2 of the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant. International Journal of Mathematics, 2019, 30 (5), pp.1950021. ⟨10.1142/S0129167X19500216⟩. ⟨hal-02320375⟩
63 Consultations
34 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More