Re: Hairy Balls and Doughnuts and the Poincare Conjecture


Michael Orion wrote:
A hairy ball must have two cowlicks if the hair is
to be laid down against the surface of the ball. A
hairy doughnut need not have any cowlicks. Do not
these two facts together prove the Poincare
Conjecture?

So... what you are asking is, are the leading
topologists of the
world are just plain dumb? For why would they have
spent
the last hundred years looking for a proof, or the
last few years
trying to understand Perelmen's...

Well, the answer to your question is a resounding NO.

-- m


Ah, now that is a bit harsh. My words were terse, but centainly not meant to suggest I thought I had found some neat little trick that great minds had somehow overlooked. I assumed the answer to my question was NO, but was hoping for a reason WHY it is no.

Nathan tells me that the Poincare conjecture is about 3-manifolds in 3D, not surfaces. But I would like a more complete understanding, perhaps with some intuitive example that is more accurate that saying a doughnot is not a ball.

- MO
.

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