Uncountably Many Inequivalent Analytic Actions of a Compact Group on A"
نویسنده
چکیده
According to a result of one of the authors [7] there are at most a countable number of inequivalent differentiable actions of a compact Lie group on a compact differentiable manifold. The results above show that both the compactness of the manifold and the differentiability of the action are necessary assumptions. In the course of our proof we also prove the following theorem, which is an elementary consequence of the recent imbedding theorem of Grauert [2], but does not seem to have been explicitly stated elsewhere. Theorem B. Let Mi and M2 be second-countable real-analytic manifolds which are diffeomorphic. Then Mi and M2 are analytically diffeomorphic.
منابع مشابه
The {L}aczkovich - {K}omjáth property for coanalytic equivalence relations
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