Perelman and the geometrization conjecture
tc...@lsa.umich.edu
Perelman claimed to be able to prove the Poincare conjecture. I noticed
today that he posted a preprint to the ArXiv last month.
http://arxiv.org/abs/math.DG/0303109
Am I right in concluding that his statements here mean that he is now *not*
claiming such a proof, if indeed he ever did claim one?
By the way, Perelman is giving a series of lectures at MIT next week, which
unfortunately I won't be able to attend.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
Greg Kuperberg
>Some time ago on this forum there was some discussion as to whether Grisha
>Perelman claimed to be able to prove the Poincare conjecture. I noticed
>today that he posted a preprint to the ArXiv last month.
>
> http://arxiv.org/abs/math.DG/0303109
>
>Am I right in concluding that his statements here mean that he is now *not*
>claiming such a proof, if indeed he ever did claim one?
At the end of his first article, math.DG/0211159, Perelman does claim
to know how to prove the Poincare conjecture, although there he only
gives a bare outline of the argument. He confirmed this in e-mail, for
instance in a message reposted at http://www.lehigh.edu/~dmd1/vk1120.txt .
Judging by the abstract, math.DG/0303109 is not a complete proof. But it
is not a retraction either. So I think that a fair summary of the arXiv
articles is that he still claims to know how to prove geometrization
and that the second article is part of the claimed proof.
--
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