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Apr 9, 2012 at 10:50 comment added Alain Valette Of course, Palais'slice theorem tells you that the answer is affirmative if the $G$-action is proper (see R. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961)).
Apr 9, 2012 at 1:25 answer added Claudio Gorodski timeline score: 3
Apr 1, 2010 at 19:41 answer added Sergei Ivanov timeline score: 8
Apr 1, 2010 at 19:39 comment added JJH Yes. This is my question.
Apr 1, 2010 at 18:41 comment added Sergei Ivanov What is "transversal slice"? Is it a small submanifold of $X$ whose tangent space at $x$ complements that of the orbit? Does "$G_x$-stable" mean "invariant under the action of $G_x$"?
Apr 1, 2010 at 16:36 history asked JJH CC BY-SA 2.5