Geometriae Dedicata

, 136:167 | Cite as

Equivariant uniformization theorem for subanalytic sets

  • Marja KankaanrintaEmail author
Original Paper


In this paper we prove an equivariant version of the uniformization theorem for closed subanalytic sets: Let G be a Lie group and let M be a proper real analytic G-manifold. Let X be a closed subanalytic G-invariant subset of M. We show that there exist a proper real analytic G-manifold N of the same dimension as X and a proper real analytic G-equivariant map \({\varphi{:} \ N \to M}\) such that \({\varphi(N) = X}\) .


Lie group Proper action Subanalytic Real analytic 

Mathematics Subject Classification (2000)



  1. 1.
    Arone, G., Kankaanrinta, M.: On the functoriality of the blow-up construction. (submitted for publication)Google Scholar
  2. 2.
    Bierstone E., Milman P.D.: Semianalytic and subanalytic sets. Inst. Hautes Études Sci. Publ. Math. 67, 5–42 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hironaka, H.: Subanalytic sets, number theory, algebraic geometry and commutative algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, pp. 454–493 (1973)Google Scholar
  4. 4.
    Kankaanrinta M.: Proper real analytic actions of Lie groups on manifolds. Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 83, 1–41 (1991)MathSciNetGoogle Scholar
  5. 5.
    Palais R.S.: On the existence of slices for actions of noncompact Lie groups. Ann. Math. 2(73), 295–323 (1961)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wasserman A.G.: Simplifying group actions. Topol. Appl. 75, 13–31 (1997)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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