The primitive lifting problem in the equivalence problem for transitive pseudogroup structures: a counterexample
HTML articles powered by AMS MathViewer
- by Pierre Molino PDF
- 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.References
- Claudette Buttin and Pierre Molino, Théorème général d’équivalence pour les pseudogroupes de Lie plats transitifs, J. Differential Geometry 9 (1974), 347–354 (French). MR 353382
- Victor Guillemin, A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Differential Geometry 2 (1968), 313–345. MR 263882
- V. W. Guillemin and S. Sternberg, The Lewy counterexample and the local equivalence problem for $G$-structures, J. Differential Geometry 1 (1967), 127–131. MR 222800
- Alan S. Pollack, The integrability problem for pseudogroup structures, J. Differential Geometry 9 (1974), 355–390. MR 353383
- I. M. Singer and Shlomo Sternberg, The infinite groups of Lie and Cartan. I. The transitive groups, J. Analyse Math. 15 (1965), 1–114. MR 217822, DOI 10.1007/BF02787690
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 224 (1976), 189-192
- MSC: Primary 58H05
- DOI: https://doi.org/10.1090/S0002-9947-1976-0426073-9
- MathSciNet review: 0426073