ON THE COMBINATORIAL STRUCTURE OF PRIMITIVE VASSILIEV INVARIANTS, III — A LOWER BOUND

Abstract

We prove that the dimension of the space of primitive Vassiliev invariants of degree n grows — as n tends to infinity — faster than [Formula: see text] for any [Formula: see text]. This solves the so-called Kontsevich–Bar–Natan conjecture. The proof relies on the use of the weight systems coming from the Lie algebra [Formula: see text] (N). In fact, we show that our bound is — up to a multiplication by a rational function in n — the best possible that one can get with [Formula: see text](N)-weight systems.