Re: Can someone please explain the Poincare Conjecture?

On Apr 14, 10:40 pm, "curious george" <bu...@xxxxxxxxx> wrote:
"Ramon F Herrera" <ra...@xxxxxxxxxxx> wrote in messagenews:b1e7060f-01f2-4140-9acc-450f89496221@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx





I was reading the Millennium Prize Problems:

http://www.claymath.org/millennium/

and I found the Poincare hard to understand. It seems that explainers
always use the apple vs. doughnut illustrative technique. What do they
mean when the say the the *only* body that can be stretched to a point
is the 2D empty sphere? Why can't an empty ovaloid be reduced
similarly?

Is it possible to visualize (i.e. draw) this stuff or is it like the
4th dimension and higher?

-Ramon

The explainers, like you called them, think that the more nebulous their
explanation is, the smartest they appear and therefore the higher they climb
in the math totem pole. However, there are people out there who are really
good at coming up with explanation that almost anyone can understand ( at
least to a degree) and I am sure that a bit of googling will provide you
with few. Try wikipedia.

In particular, try this page:
http://tinyurl.com/ca3fcy

If you still want more, try reading
the first few pages of this book,
available free online:

http://arxiv.org/abs/math.DG/0607607

"This manuscript contains a detailed
proof of the Poincare Conjecture. The
arguments we present here are expanded
versions of the ones given by Perelman
in his three preprints posted in 2002
and 2003."

Just reading the introduction and
"Overview of Perelman's Argument"
(first 5 pages) gives you some idea
of what Perelman did.

.

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