Asymptotic Vassiliev Invariants for Vector Fields

2008/10/21 by Sebastian Baader, Julien Marché, Baader, Sebastian +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #math.DS #math.GT #msc:37A05 #msc:57M27

paper · pdf · doi:10.48550/arxiv.0810.3870

12 pages, 3 figures

arxiv created 2008/10/21 · arxiv updated 2009/12/01

Abstract

We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of \R³. 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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