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Ricci Flow and the Poincaré Conjecture

  • Steven G. Krantz
  • Harold R. Parks
Chapter

Abstract

Jules Henri Poincaré (1854–1912) was one of the great geniuses of nineteenth and twentieth-century mathematics. Born into a distinguished family of academicians and public servants, he showed early talent in mathematics and science. Indeed, the entire country of France watched in awe as Poincaré developed from a child prodigy to a major leader in mathematics and physics.

Keywords

Steklov Institute Rubber Band Mathematical Community Geometrization Program Ricci Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References and Further Reading

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    Cao, H.-D., Zhu, X.-P.: A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow. Asian Journal of Mathematics 10, 165–498 (2006)CrossRefMATHMathSciNetGoogle Scholar
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    Kuhn, T.S.: The Structure of Scientific Revolutions, 2nd edn. University of Chicago Press, Chicago (1970)Google Scholar
  4. [MT 07]
    Morgan, J., Tian, G.: Ricci flow and the Poincaré conjecture. In: Clay Mathematics Monographs, American Mathematical Society, Providence (2007)Google Scholar
  5. [MT 08]
    Morgan, J., Tian, G.: Completion of the proof of the geometrization conjecture. arXiv:0809.4040v1[math.DG]Google Scholar
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    Perelman, G.: The entropy formula for the Ricci flow and its geometric applications (2008). arXiv:math.DG/0211159v1Google Scholar
  7. [Per(b)]
    Perelman, G.: Ricci flow with surgery on three-manifolds (2008). arXiv:math.DG/0303109v1Google Scholar
  8. [Per(c)]
    Perelman, G.: Finite extinction time for the solutions to the Ricci flow on certain three-manifolds (2008). arXiv:math.DG/ 0307245v1Google Scholar
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    Poincaré, H.: Cinquième complément á l’analysus situs. In: Œuvres de Poincaré, pp. 435–498. Gauthier-Villars, Tome. VI, Paris (1953). Originally published in Rendiconti de Circolo Matematica di Palermo, 18 (1904), 45–110Google Scholar
  10. [Strz 06]
    Strzelecki, P.: The Poincaré conjecture? American Mathematical Monthly 113, 75–78 (2006)CrossRefMATHMathSciNetGoogle Scholar
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    Thurston, W.P.: The Geometry and Topology of Three- Manifolds. Notes. Princeton University, Princeton, NJ (1980)Google Scholar
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Steven G. Krantz
    • 1
  • Harold R. Parks
    • 2
  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvalisUSA

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