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Topic: Poincare Conjecture
Replies: 8   Last Post: Sep 17, 2006 2:03 PM

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Chan-Ho Suh

Posts: 425
Registered: 12/10/04
Re: Poincare Conjecture
Posted: Sep 17, 2006 8:59 AM
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In article <ee60bf$ko8$1@panix2.panix.com>,
lrudolph@panix.com (Lee Rudolph) wrote:

> The difficult theorem I referred to is a theorem of, I think, Bing (or
> maybe Moise, or maybe someone else in that circle--don't make me look
> for it!) to the effect that a 3-manifold M is simply connected if and
> only if every knot in M is contained in a 3-ball in M. That is *very*
> non-obvious...


Yes, because it proves the Poincare conjecture if you use the following
theorem of Bing:

A closed, connected 3-manifold is the 3-sphere if and only if every knot
lies in a 3-ball.

:-)



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