High-dimensional helicities and rigidity of linked foliations.
type: Item
instance of: scholarly article
title: High-dimensional helicities and rigidity of linked foliations.
zbMATH Open document ID: 1045.57017
author: Tristan Rivière
published in: The Asian Journal of Mathematics
publication date: 2003-10-09T00:00:00Z
review text: The paper opens with a very brief description of work of \textit{M. H. Freedman} and \textit{Z.-X. He} [Ann. Math. (2) 134, No. 1, 189--229 (1991; Zbl 0746.57011)] on the generalized Hopf invariant and rigidity of knotted magnetic tubes. The work by Freedman and He builds on earlier ideas of \textit{V. I. Arnol'd} [Sel. Math. Sov. 5, 327--345 (1986; Zbl 0623.57016)], who termed the generalized Hopf invariant \textit{helicities} in this context, and even earlier work by \textit{S. P. Novikov} [Russ. Math. Surv. 39, No. 5, 113--124 (1984; Zbl 0619.58002)]. The present author gives an ergodic interpretation of Hopf-Novikov helicities as conjectured by Arnol'd. Furthermore, the topological bounds obtained by Freedman and He for energies of invariant forms of linked foliations are extended to higher dimensions.
reviewed by: Vagn Lundsgaard Hansen
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 57Q25
zbMATH DE Number: 1925770
zbMATH Keywords: Hopf-Novikov helicities
zbMATH Keywords: energies
zbMATH Keywords: foliations
MaRDI profile type: Publication
full work available at URL: ajm.2002.v6.n3.a6
OpenAlex ID: W2734102861
DOI: 10.4310/AJM.2002.V6.N3.A6
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description: scientific article; zbMATH DE number 1925770