The number of primitive Vassiliev invariants up to degree 12

Abstract

We present algorithms giving upper and lower bounds for the number of independent primitive rational Vassiliev invariants of degree m modulo those of degree m-1. The values have been calculated for the formerly unknown degrees m = 10, 11, 12. Upper and lower bounds coincide, which reveals that all Vassiliev invariants of degree smaller 13 are orientation insensitive and are coming from representations of Lie algebras so and gl. Furthermore, a conjecture of Vogel is falsified and it is shown that the Λ-module of connected trivalent diagrams (Chinese characters) is not free.

18 pages, latex, 30 postscript figures (uses epsf.tex), the paper is available at http://rhein.iam.uni-bonn.de/~jk/index.html

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