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Complete Solution of Poincare Conjecture

  1. Jul 28, 2006 #1

    selfAdjoint

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    Announced in this paper. Differential Geometry meets Geometric Surgery on three-manifolds; Perelman clarified and (perhaps) corrected.


    A COMPLETE PROOF OF THE POINCAR´E AND GEOMETRIZATION CONJECTURES – APPLICATION OF THE HAMILTON-PERELMAN THEORY OF THE RICCI FLOW

    HUAI-DONG CAO† AND XI-PING ZHU


    Abstract. "In this paper, we give a complete proof of the Poincar´e and the geometrization conjectures. This work depends on the accumulative works of many geometric analysts in the past thirty years. This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow. "

    The first sections give a clear history of the recent approaches to the Poincare Conjecture and Thurman's Geometric Conjecture, which are joined at the hip. The guy who I feel sorry for is Hamilton, who did fantastic things to lay almost all of the groundwork for the solution but, like Moses, was not able to enter the promised land.
     
    Last edited: Jul 28, 2006
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  3. Jul 28, 2006 #2
  4. Jul 28, 2006 #3

    selfAdjoint

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    Right. I should have made it clear that's where I got the link to the Cao and Zhu paper from.

    While I fully expect the actual proof to be over my head, and I can't hope to maike it through all 200 + pages, the historical account and the general idea of what they're doing is pretty clear to me.
     
  5. Jul 28, 2006 #4
    Even that's waaay over my head. :biggrin:
     
  6. Aug 16, 2006 #5

    robphy

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  7. Aug 21, 2006 #6
  8. Aug 21, 2006 #7
    Why does it start at page 165? What are on the previous pages?
     
  9. Aug 21, 2006 #8
    That's because it's been taken from a journal.
     
  10. Aug 21, 2006 #9
    Last two sentences.

    "Hence in case (2), M is diffeomorphic to a flat manifold and then it is also geometrizable.

    Therefore we completed the proof of the theorem. "


    That's a million dollar conclusion, heh.
     
  11. Aug 21, 2006 #10
    Welcome to modern mathematics.
     
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