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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Pierre Molino
Journal: Trans. Amer. Math. Soc. 224 (1976), 189-192
MSC: Primary 58H05
MathSciNet review: 0426073
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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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Keywords: Equivalence problem, almost-$ \Gamma $-structures, primitive Lie pseudogroups, Lewy counterexample, equivalence theorem, flat pseudogroups, primitive lifting theorem
Article copyright: © Copyright 1976 American Mathematical Society

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