SEMIALGEBRAIC G CW COMPLEX STRUCTURE OF SEMIALGEBRAIC G SPACES

  • Park, Dae-Heui ;
  • Suh, Dong-Youp
  • Published : 1998.05.01

Abstract

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