The primitive lifting problem in the equivalence problem for transitive pseudogroup structures: a counterexample

Molino, Pierre

doi:10.1090/S0002-9947-1976-0426073-9

The primitive lifting problem in the equivalence problem for transitive pseudogroup structures: a counterexample
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Trans. Amer. Math. Soc. 224 (1976), 189-192 Request permission

Abstract:

A transitive Lie pseudogroup ${\Gamma _M}$ on M is a primitive extension of ${\Gamma _N}$ if ${\Gamma _N}$ is the quotient of ${\Gamma _M}$ by an invariant fibration $\pi :M \to N$ and if the pseudogroup induced by ${\Gamma _M}$ on the fiber of $\pi$ is primitive. In the present paper an example of this situation is given with the following property (counterexample to the primitive lifting property): the equivalence theorem is true for almost-${\Gamma _N}$-structures but false for almost-${\Gamma _M}$-structures.

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