On the asymptotic linking number

Vogel, Thomas

doi:10.1090/S0002-9939-02-06792-8

On the asymptotic linking number
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Proc. Amer. Math. Soc. 131 (2003), 2289-2297 Request permission

Abstract:

We prove a theorem formulated by V. I. Arnold concerning a relation between the asymptotic linking number and the Hopf invariant of divergence–free vector fields. Using a modified definition for the system of short paths, we prove their existence in the general case.

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