In article <email@example.com>, firstname.lastname@example.org (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.