On the Combinatorial Structure of Primitive Vassiliev Invariants, III - A Lower Bound

Details On the Combinatorial Structure of Primitive Vassiliev Invariants, III - A Lower Bound On the Combinatorial Structure of Primitive Vassiliev Invariants, III - A Lower Bound

1998-06-16

arxiv.org/abs/math/9806086v1

Commun. Contemp. Math. 2 (2000), no. 4, 579--590

Mathematics

Geometric Topology

11 pages, 12 figures

Scientific paper

We prove that the dimension of the space of primitive Vassiliev invariants of degree n grows - as n tends to infinity - faster than Exp(c Sqrt(n)) for any c < Pi Sqrt (2/3). The proof relies on the use of the weight systems coming from the Lie algebra gl(N). In fact, we show that our bound is - up to multiplication with a rational function in n - the best possible that one can get with gl(N)-weight systems.

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