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On the asymptotic linking number

Author: Thomas Vogel
Journal: Proc. Amer. Math. Soc. 131 (2003), 2289-2297
MSC (2000): Primary 57R25; Secondary 37C10, 57R30, 76W05
Published electronically: October 24, 2002
MathSciNet review: 1963779
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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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Additional Information

Thomas Vogel
Affiliation: Mathematisches Institut, Universität München, Theresienstr. 39, 80333 München, Germany

Received by editor(s): October 29, 2001
Received by editor(s) in revised form: February 25, 2002
Published electronically: October 24, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society