Has the Poincaré conjecture been proved?

Question

if it has been proven...how is it important to the field of mathematics??

Answer 1

The experts seem to agree that it has been solved. In fact, a more general result called the 'Geometrization Conjecture' was proven. This was done in an unpublished manuscript done by Perleman and subsequently 'cleaned up' by Yau. This really opens up a lot of possibilities in the study of three dimensional manifolds. In particular, the geometrization conjecture allows the classification of three manifolds as objects obtained by'patching together' a few basic, known, pieces.

Answer 2

In July 2006, John Morgan of Columbia University and Gang Tian of the Massachusetts Institute of Technology posted a paper on the arXiv titled, "Ricci Flow and the Poincaré Conjecture." In this paper, they claim to provide a "detailed proof of the Poincaré Conjecture".[10]

Answer 3

It sounds like it relatively is been proved via a mathematician named Perelman. I in simple terms study that yet another mathematician has gotten smaller to place in writing a e book approximately Perelman's evidence and is very virtually complete with that e book.the challenge is that Perelmen is tremendously secretive and isn't any longer doing the formal write-up himself. At this factor, no one has got here across an blunders and the uncomplicated concept seems stable.

Answer 4

I believe the results of Perelman, which imply the Poincare Conjecture, have with stood all review thus far.

Answer 5

Hi. Not yet. Manifold topology is pretty hard to prove..