"Jon Perry" <perry@globalnet.co.uk> writes:
Thanks - I can see the weaknesses in my argument.
Very good, if true.
However, is there anything wrong with this;
PC is true because from the 3-sphere, a compact, simply connected manifold, through only operations which preserve homeomorphicity, we can attain every other compact, simply-connected 3-manifold.
Yes, there's something wrong with that. Any statement of the form "PC is true because <sentence>" is hogwash. If you were going to prove PC, you would need more than a sentence to express a convincing proof. It might be accurate to say "If I could prove <sentence>, that would imply PC". That depends on the sentence, of course. If you ever convinced someone that you might have a proof of PC, then it might be appropriate to say something of the form, "I have proved <sentence>, and that implies PC." But you made the statement in the hogwash form. Moreover, you made that statement in reply to a message that shows that you not only did not present a realistic approach to a proof of PC, but were apparently unclear on the concept of what a proof of PC would be, and that you were beginning to sound like a crank. I hope your statement is not a proof, because it certainly isn't a proof of the Poincare conjecture. Dan Hoey Hoey@AIC.NRL.Navy.Mil