Title: 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.