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The existence of semialgebraic slices and its applications

서동엽|Dae Heui Park|Myung-Jun Choi
대한수학회 (The Korean Mathematical Society)|2004.07|대한수학회지 (Journal of the KMS)|제41권 제4호|pp. 629-646

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Abstract

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

참고문헌 (14)

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  2. "Introduction to Compact Transformation Groups", 46 (1972), Academic Press
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  4. "Lecture Notes in Math.1173" (1985), Springer-Verlag
  5. "Space with a compact Lie group of transformations", 1, pp.35~43 (1950)
  6. "Triangulations of algebraic varieties", 29, pp.165~185 (1975)
  7. "Triangulation of semi-analytic sets", pp.474~ (1964)
  8. "The existence of a slice Ann. of Math.63" (1957)
  9. "Equivariant embeddings in Euclidean space", pp.446~ (1957)
  10. "Imbedding of compact dierential transformation groups in orthog-onal representations", 6, pp.673~678 (1957)
  11. "The classication ofG-spaces", 36 (1960)
  12. "Equivariant semi-algebraic triangulation of real alge-braic G-varieties", 50(1), pp.179~205 (1996)
  13. "Equivariant semialgebraic homotopies", 115, pp.153~174 (2001)
  14. "Linear embeddings of semialgebraicG-spaces", 242(4), pp.725~742 (2002)

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