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.