. Dans-les-deux-cas, il est nécessaire de considérer des 3-variétés M contenant un entrelacs non vide L (qui sertàsertà modifier les poids de la somme) sans quoi la somme d'´ etats s'annule. Nous utilisons dans les sections suivantes des idées en partie analogues pour définir des, ?) de triplets (une 3-variété orienté M , un entrelacs L ? M , une représentation du groupe ? 1 (M, * ))

L. 'image-par-z-d-'un, N-gradué de dimension infini donné par une présentation. Les générateurs de cet espace sont des diagrammes de Feynman Rozansky a conjecturé que Z(K) appartientàappartientà l'image de l'application ?cheveux ? : On peut définir un espace engendré par des diagrammes de Feynman avec perles. Ces perles sont une décoration des arêtes des diagrammes par des entiers. L'application ? cheveux ? H substituè a ces perles des arêtes, produisant des séries formelles de diagrammes de Feynman. Kricker a prouvé la conjecture de Rozansky puis a montré directement avec Garoufalidis l'existence d'un

G. Rozansky and . Et-kricker-ont-conjecturé-que-h-pourraitêtrepourraitêtre-injective, Dans [54], nous montrons que ce n'est pas le cas. Nous utilisons un diviseur de zéro découvert par Vogel dans son algèbre ? (cf [68]) pour construire unélémentunélément dans le noyau de l'application H. Nous introduisons une graduation

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