Complete Solution of Poincare Conjecture

  • #1
selfAdjoint
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Main Question or Discussion Point

Announced in http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-165-492.pdf" [Broken]. 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.
 
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  • #3
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neutrino said:
I don't understand an iota of all this, but here's some related discussion at NEW
http://www.math.columbia.edu/~woit/wordpress/?p=434

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.
 
  • #4
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selfAdjoint said:
the historical account and the general idea of what they're doing is pretty clear to me.
Even that's waaay over my head. :biggrin:
 
  • #7
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Why does it start at page 165? What are on the previous pages?
 
  • #8
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That's because it's been taken from a journal.
 
  • #9
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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.
 
  • #10
waht said:
That's a million dollar conclusion, heh.
Welcome to modern mathematics.
 

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