Arkiv för Matematik

  • Ark. Mat.
  • Volume 50, Number 1 (2012), 165-182.

Persistence of freeness for Lie pseudogroup actions

Peter J. Olver and Juha Pohjanpelto

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Abstract

The action of a Lie pseudogroup $\mathcal{G}$ on a smooth manifold M induces a prolonged pseudogroup action on the jet spaces Jn of submanifolds of M. We prove in this paper that both the local and global freeness of the action of $\mathcal{G}$ on Jn persist under prolongation in the jet order n. Our results underlie the construction of complete moving frames and, indirectly, their applications in the identification and analysis of the various invariant objects for the prolonged pseudogroup actions.

Note

Peter Olver was supported in part by NSF Grant 08-07317.

Article information

Source
Ark. Mat., Volume 50, Number 1 (2012), 165-182.

Dates
Received: 11 January 2010
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907156

Digital Object Identifier
doi:10.1007/s11512-010-0133-1

Mathematical Reviews number (MathSciNet)
MR2890349

Zentralblatt MATH identifier
1260.58010

Rights
2011 © Institut Mittag-Leffler

Citation

Olver, Peter J.; Pohjanpelto, Juha. Persistence of freeness for Lie pseudogroup actions. Ark. Mat. 50 (2012), no. 1, 165--182. doi:10.1007/s11512-010-0133-1. https://projecteuclid.org/euclid.afm/1485907156


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