Arkiv för Matematik

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

Persistence of freeness for Lie pseudogroup actions

Peter J. Olver and Juha Pohjanpelto

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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.


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

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

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

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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.

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