Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE EXISTENCE OF SEMIALGEBRAIC SLICES AND ITS APPLICATIONS

  • Choi, Myung-Jun (Department of Mathematics Korea Advanced Institute of Science and Technology) ;
  • Park, Dae-Heui (Department of Mathematics College of Natural Sciences Chonnam National University) ;
  • Suh, Dong-Youp (Department of Mathematics Korea Advanced Institute of Science and Technology)
  • Published : 2004.07.01
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Abstract

Let G be a compact semialgebraic group and M a semi-algebraic G-set. We prove that there exists a semialgebraic slice at every point of M. Moreover M can be covered by finitely many semialgebraic G-tubes. As an application we give a different proof that every semialgebraic G-set admits a semi algebraic G-embedding into some semialgebraic orthogonal representation space of G, which has been proved in [15].

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References

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  1. Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem vol.154, pp.1, 2007, https://doi.org/10.1016/j.topol.2006.03.017
  2. SLICE THEOREM FOR SEMIALGEBRAICALLY PROPER ACTIONS vol.37, pp.4, 2015, https://doi.org/10.5831/HMJ.2015.37.4.431