Asymptotic Vassiliev invariants for vector fields

Sebastian Baader; Julien Marché

Bulletin de la Société Mathématique de France (2012)

  • Volume: 140, Issue: 4, page 569-582
  • ISSN: 0037-9484

Abstract

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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.

How to cite

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Baader, Sebastian, and Marché, Julien. "Asymptotic Vassiliev invariants for vector fields." Bulletin de la Société Mathématique de France 140.4 (2012): 569-582. <http://eudml.org/doc/272714>.

@article{Baader2012,
abstract = {We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of $\mathbb \{R\}^3$. More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field.},
author = {Baader, Sebastian, Marché, Julien},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Vassiliev invariants; helicity; Gauss diagram},
language = {eng},
number = {4},
pages = {569-582},
publisher = {Société mathématique de France},
title = {Asymptotic Vassiliev invariants for vector fields},
url = {http://eudml.org/doc/272714},
volume = {140},
year = {2012},
}

TY - JOUR
AU - Baader, Sebastian
AU - Marché, Julien
TI - Asymptotic Vassiliev invariants for vector fields
JO - Bulletin de la Société Mathématique de France
PY - 2012
PB - Société mathématique de France
VL - 140
IS - 4
SP - 569
EP - 582
AB - We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of $\mathbb {R}^3$. More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field.
LA - eng
KW - Vassiliev invariants; helicity; Gauss diagram
UR - http://eudml.org/doc/272714
ER -

References

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  1. [1] V. I. Arnold & B. A. Khesin – Topological methods in hydrodynamics, Applied Mathematical Sciences, vol. 125, Springer, 1998. Zbl0902.76001MR1612569
  2. [2] S. Baader – « Asymptotic link invariants for ergodic vector fields », preprint arXiv:math.GT/0803.0898. 
  3. [3] J.-M. Gambaudo & É. Ghys – « Signature asymptotique d’un champ de vecteurs en dimension 3 », Duke Math. J.106 (2001), p. 41–79. Zbl1010.37010MR1810366
  4. [4] S. Garoufalidis & A. Kricker – « A rational noncommutative invariant of boundary links », Geom. Topol.8 (2004), p. 115–204. Zbl1075.57004MR2033481
  5. [5] M. Goussarov, M. Polyak & O. Viro – « Finite-type invariants of classical and virtual knots », Topology39 (2000), p. 1045–1068. Zbl1006.57005MR1763963
  6. [6] J. Marché – « A computation of the Kontsevich integral of torus knots », Algebr. Geom. Topol.4 (2004), p. 1155–1175. Zbl1082.57009MR2113901
  7. [7] M. Polyak & O. Viro – « Gauss diagram formulas for Vassiliev invariants », Int. Math. Res. Not. 1994 (1994), p. 445ff., approx. 8 pp. Zbl0851.57010MR1316972
  8. [8] T. Vogel – « On the asymptotic linking number », Proc. Amer. Math. Soc.131 (2003), p. 2289–2297. Zbl1015.57018MR1963779

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