Abstract
Let be a Lie group, and let be a smooth proper -manifold. Let denote the orbit space, and let be the natural map. It is known that is homeomorphic to a polyhedron. In the present paper we show that there exist a piecewise linear (PL) manifold , a polyhedron , and homeomorphisms and such that is PL. This is an application of the theory of subanalytic sets and subanalytic maps of Shiota. If and the -action are, moreover, subanalytic, then we can choose and subanalytic and and unique up to PL homeomorphisms.
Citation
Mitsutaka Murayama. Masahiro Shiota. "Triangulation of the map of a -manifold to its orbit space." Nagoya Math. J. 212 159 - 195, December 2013. https://doi.org/10.1215/00277630-2366201
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