Persistence of freeness for Lie pseudogroup actions. (English) Zbl 1260.58010

Olver, Peter J.; Pohjanpelto, Juha

Ark. Mat. 50, No. 1, 165-182 (2012).

The concept of action is one of the useful tools in algebraic and differential topology. In this paper, the authors deal with the action of a Lie pseudogroup on a smooth manifold and its moving frames and invariants. More precisely, the action of a Lie pseudogroup \(G\) on a smooth manifold \(M\) induces a prolonged pseudogroup action on the jet spaces of submanifolds of \(M\). Using this fact, the authors prove that both the local and global freeness of the action of \(G\) on the jet space \(J^n\) persist under prolongation of the pseudogroup action at the jet order \(n\).

Reviewer: M. Habil Gürsoy (Malatya)

MSC:

58H05	Pseudogroups and differentiable groupoids
22A22	Topological groupoids (including differentiable and Lie groupoids)
58A20	Jets in global analysis

Keywords:

Lie pseudogroup; action; moving frame

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