Open Access
April 2012 Persistence of freeness for Lie pseudogroup actions
Peter J. Olver, Juha Pohjanpelto
Author Affiliations +
Ark. Mat. 50(1): 165-182 (April 2012). DOI: 10.1007/s11512-010-0133-1


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.

Funding Statement

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


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Peter J. Olver. Juha Pohjanpelto. "Persistence of freeness for Lie pseudogroup actions." Ark. Mat. 50 (1) 165 - 182, April 2012.


Received: 11 January 2010; Published: April 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1260.58010
MathSciNet: MR2890349
Digital Object Identifier: 10.1007/s11512-010-0133-1

Rights: 2011 © Institut Mittag-Leffler

Vol.50 • No. 1 • April 2012
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