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Pursell-Shanks type theorem for orbit spaces of G-manifolds. (English) Zbl 0519.57033


MSC:

57S15 Compact Lie groups of differentiable transformations
57R25 Vector fields, frame fields in differential topology
17B65 Infinite-dimensional Lie (super)algebras
57R50 Differential topological aspects of diffeomorphisms
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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References:

[1] Amemiya, I., Lie algebra of vector fields and complex structure., J. Math. Soc. Japan, 27 (1975), 545-549. · Zbl 0311.57012
[2] Bierstone, E., Lifting isotopies from orbit spaces, Topology, 14 (1975), 245-252. · Zbl 0317.57015
[3] Davis, M., Smooth G-manifolds as collections of fibre bundles, Pacific J. Math., 77 (1978), 315-363. · Zbl 0403.57002
[4] Fukui, K., Pursell-Shanks type theorem for free G-manifolds, Publ. Res. Inst. Math. Set., 17 (1981), 249-265. · Zbl 0464.57018
[5] Koriyama, A., On Lie algebras of vector fields with invariant submanif olds, Nagoya J. Math., 55 (1974), 91-110. · Zbl 0273.22016
[6] Omori, H., Infinite dimensional Lie transformation groups, Lecture Notes in Math., 427 Springer-Verlag, 1976. · Zbl 0328.58005
[7] Poenaru, V., Singularite C^\circ ^\circ en presence de symetrie, Lecture Notes in Math., 510 Springer-Verlag, 1976.
[8] Pursell, L. E. and Shanks, M. E., The Lie algebra of a smooth manifold, Proc. Amer. Math. Soc., 5 (1954), 468-472. · Zbl 0055.42105
[9] Schwarz, G. W., Smooth invariant functions under the action of a compact Lie group, Topology, 14 (1975), 63-68. · Zbl 0297.57015
[10] , Covering smooth homotopies of orbit spaces, Bull. Amer. Math. Soc., 83 (1977), 1028-1030. · Zbl 0369.57018
[11] f Lifting smooth homotopies of orbit spaces, Inst. Hautes Etudes Set. Publ. Math., 51 (1980), 37-135. · Zbl 0449.57009
[12] Sternberg, S., Local contractions and a theorem of Poincare”, Amer. J. Math., 79 (1957), 809-824. · Zbl 0080.29902
[13] Takeuchi, M., Modern Spherical functions, Iwanami-Shoten, 1975. (in Japanese)
[14] Weyl, H., The Classical Groups, 2nd edition, Princeton, Univ. Press, Princeton, New Jersey, 1973.
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