This article is cited in 10 papers

Geometry of higher helicities

B. A. Khesin

Department of Mathematics, University of Toronto

Abstract: We revisit an interpretation of higher-dimensional helicities and Hopf–Novikov invariants from the point of view of the Brownian ergodic theorem. We also survey various results related to Arnold's theorem on the asymptotic Hopf invariant on three-dimensional manifolds and recent work on linking of a vector field with a foliation, the asymptotic crossing number, short path systems, and relations with the Calabi invariant.

Key words and phrases: Asymptotic Hopf invariant, linking number, linking form, measured foliation, ergodic theorems.

MSC: 37A15, 55Q25, 76W05

Received: April 4, 2003

Language: English

DOI: 10.17323/1609-4514-2003-3-3-989-1011

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