On a Theorem of Montgomery and Samelson
نویسنده
چکیده
In their paper on fibrations with singularities Montgomery and Samelson showed that if a compact connected Lie group acts differentiably and effectively on a sphere and if there is one stationary point, then the remaining orbits cannot all be of the same dimension [2]. In our note we will examine transformation groups in which all orbits have the same dimension. As a corollary, we shall extend the Montgomery-Samelson theorem to all closed simply connected manifolds. We shall not use a differentiability hypothesis. We shall denote by (L, X) the action of a compact, connected Lie group L on a locally compact connected separable metric space X. It will be assumed that all the orbits of (L, X) have the same dimension. We denote by
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