Abstract
In view of the result of Kontsevich, now often called "the fundamental theorem of Vassiliev theory", identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear span of chord diagrams modulo the "4T-relation" (and in the unframed case, originally considered by Vassiliev, the "1T-" or "isolated chord relation"), it is a problem of some interest to provide a basis for the space of chord diagrams modulo the 4T-relation. We construct the basis for the vector space spanned by chord diagrams with n chords and m link components, modulo 4T relations for n ≤ 5.
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