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We extend V. Arnold's theory of asymptotic linking for two volume preservingflows on a domain in ${\mathbb R}^3$ and $S^3$ to volume preserving actions of${\mathbb R}^k$ and ${\mathbb R}^\ell$ on certain domains in ${\mathbb R}^n$and also to linking of a volume preserving action of ${\mathbb R}^k$ with aclosed oriented singular $\ell$-dimensional submanifold in ${\mathbb R}^n$,where $n=k+\ell+1$. We also extend the Biot-Savart formula to higherdimensions.

Asymptotic linking of volume-preserving actions of ${\mathbb R}^k$