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

Abstract : 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.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02320375
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 18 octobre 2019 - 16:19:18
Dernière modification le : jeudi 23 janvier 2020 - 18:22:13

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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, World Scientific Publishing, 2019, 30 (5), pp.1950021. ⟨10.1142/S0129167X19500216⟩. ⟨hal-02320375⟩

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