Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58H05

Retrieve articles in all journals with MSC: 58H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0426073-9
PII: S 0002-9947(1976)0426073-9
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