Inventiones mathematicae

, Volume 107, Issue 1, pp 87–98 | Cite as

On approximating submanifolds by algebraic sets and a solution to the Nash conjecture

  • S. Akbulut
  • H. King
Article

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References

  1. [AK1] Akbulut, S., King, H.: The topology of real algebraic sets with isolated singularities. Ann. Math.113, 425–446 (1981)Google Scholar
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  3. [AK3] Akbulut, S., King, H.: Submanifolds and homology of nonsingular real algebraic varieties. Am. J. Math.107, 45–84 (1985)Google Scholar
  4. [AK4] Akbulut, S., King, H.: Algebraicity of Immersions in ℝn. (to appear)Google Scholar
  5. [BT] Benedetti, R., Tognoli, A.: On real algebraic vector bundles. Bull. Sci. Math., II. Sér.104, 89–112 (1980)Google Scholar
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  7. [K] King, H.: Approximating submanifolds of real projective space by varieties. Topology15, 81–85 (1976)Google Scholar
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  9. [N] Nash, J.: Real Algebraic Manifolds. Ann. Math.56, 405–421 (1952)Google Scholar
  10. [S] Shaferevich, I.R.: Basic Algebraic Geometry. Berlin Heidelberg New York: Springer 1977Google Scholar
  11. [T1] Tognoli, A.: Any compact differentiable submanifold of ℝn has an algebraic approximation in ℝn. Topology27, 205–210 (1988)Google Scholar
  12. [T2] Tognoli, A.: Algebraic approximation of manifolds and spaces. Séminaire Bourbaki, 32éme aneé, No. 548, 1979Google Scholar
  13. [W] Wallace, A.: Algebraic approximations of manifolds. Proc. Lond. Math. Soc.7, 196–210 (1957)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • S. Akbulut
    • 1
  • H. King
    • 2
  1. 1.Department of MathematicsMichigan State UniversityE. LansingUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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