The number of primitive Vassiliev invariants up to degree 12

Details The number of primitive Vassiliev invariants up to degree 12 The number of primitive Vassiliev invariants up to degree 12

1997-06-18

arxiv.org/abs/q-alg/9706022v1

Mathematics

Quantum Algebra

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

Scientific paper

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 \Lambda-module of connected trivalent diagrams (Chinese characters) is not free.

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