10
13. 9. 2013.
On volume-preserving vector fields and finite-type invariants of knots
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.