J. Korean Math. Soc. 1998; 35(2): 371-386
Printed June 1, 1998
Copyright © The Korean Mathematical Society.
Dae Heui Park and Dong Youp Suh
KAIST and KAIST
Let $G$ be a compact Lie group and $M$ a semialgebraic $G$ space in some orthogonal representation space of $G$. We prove that if $G$ is finite then $M$ has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When $G$ is not finite we show that $M$ has a semialgebraic $G$ $CW$ complex structure, and this structure is unique. As a consequence compact semialgebraic $G$ space has an equivariant simple homotopy type.
Keywords: action, semialgebraic set, triangulation, $CW$ complex structure, algebraic variety
MSC numbers: 14P10, 22E99, 57Q91
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