At 06:44 AM 10/9/03 -0400, you wrote:
A good external criticism of this argument is that it applies equally to all 3-manifolds. It doesn't mention or use the condition that the manifold is simply-connected, so if there weren't a flaw it would show that the 3-sphere is the only 3-manifold (and that 2 + 2 = 3, etc.)
I don't think Dan Asimov would make an error that blatant. I had presumed that the assumption of simple connectivity was discharged behind one or both of the two fig-leaves in his synopsis, marked by the two occurrences of the phrase "a simple argument shows ...".
Internally, the problem is that not all trajectories have to enter or exit through the boundary. For instance, there may be circular trajectories of the vector field.
If this were the problem, it would be hidden in Dan's second "simple argument", which purports to demonstrate that the structure of the altered manifold is S^2 x [0,1]. As I stated before, Dan's presentation seems to imply that the flaw is in the open, not in one of the omitted simple arguments. -A