Asymptotic Vassiliev Invariants for Vector Fields

Details Asymptotic Vassiliev Invariants for Vector Fields Asymptotic Vassiliev Invariants for Vector Fields

2008-10-21

arxiv.org/abs/0810.3870v1

Mathematics

Geometric Topology

12 pages, 3 figures

Scientific paper

We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of $\R^3$. More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field. As an application, we determine the asymptotic Alexander and Jones polynomials and give a formula for the asymptotic Kontsevich integral.

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