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On volume-preserving vector fields and finite-type invariants of knots

Published online by Cambridge University Press:  06 November 2014

R. KOMENDARCZYK  and
I. VOLIĆ
R. KOMENDARCZYK
Affiliation:
Tulane University, New Orleans, LA 70118, USA email rako@tulane.edu
I. VOLIĆ
Affiliation:
Wellesley College, Wellesley, MA 02481-8203, USA email ivolic@wellesley.edu
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Abstract

We consider the general non-vanishing, divergence-free vector fields defined on a domain in $3$-space and tangent to its boundary. Based on the theory of finite-type invariants, we define a family of invariants for such fields, in the style of Arnold’s asymptotic linking number. Our approach is based on the configuration space integrals due to Bott and Taubes.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 832 - 859
Copyright
© Cambridge University Press, 2014 

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