On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams

Details On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams

2008-01-21

arxiv.org/abs/0801.3253v1

Mathematics

Geometric Topology

25 papers, numerous png figures

Scientific paper

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, 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 distinguishable link components, modulo 4T relations for n less than or equal to 5.

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