TRIANGULATION OF THE MAP OF A G-MANIFOLD TO ITS ORBIT SPACE
| Autor: | Masahiro Shiota, Mitsutaka Murayama |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Triangulation (topology)
General Mathematics Lie group Geometric Topology (math.GT) 57S15 57S20 58K20 Space (mathematics) 58K20 Manifold Piecewise linear function Combinatorics Mathematics::Logic Polyhedron Mathematics - Geometric Topology 57S20 FOS: Mathematics Orbit (control theory) 57S15 Mathematics |
| Zdroj: | Nagoya Math. J. 212 (2013), 159-195 |
| Popis: | Let G be a Lie group, and let M be a smooth proper G-manifold. Let M/G denote the orbit space, and let π : M → M/G be the natural map. It is known that M/G is homeomorphic to a polyhedron. In the present paper we show that there exist a piecewise linear (PL) manifold P, a polyhedron L, and homeomorphisms τ : P → M and σ : M/G → L such that σ o π o τ is PL. This is an application of the theory of subanalytic sets and subanalytic maps of Shiota. If M and the G-action are, moreover, subanalytic, then we can choose τ and σ subanalytic and P and L unique up to PL homeomorphisms. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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