Abstract
AbstractLetGbe a Lie group, and letMbe a smooth properG-manifold. LetM/Gdenote the orbit space, and letπ:M → M/Gbe the natural map. It is known thatM/Gis homeomorphic to a polyhedron. In the present paper we show that there exist a piecewise linear (PL) manifoldP,a polyhedronL, and homeomorphismsτ:P → Mandσ:M/G → Lsuch thatσ o π o τis PL. This is an application of the theory of subanalytic sets and subanalytic maps of Shiota. IfMand theG-action are, moreover, subanalytic, then we can chooseτandσsubanalytic andPandLunique up to PL homeomorphisms.
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