Talk:Anti-knot

Is "Proof 1" really a proof? I don't see it. It states the obvious but doesn't exclude the possibility of a non-obvious configuration that is equivalent to the unknot. Proof 2 has the feel of the minimal acceptable proof based on my experience with topology. Before I go looking in the references to see if they give this proof, can anyone correct me? Ryan Reich 17:26, 26 December 2006 (UTC)[reply]

"Proof 1" is bogus, clearly. Much more needs to be said. For example, one can use the associativity of the knot sum extended to an infinite sum, the typical "Mazur swindle" kind of argument.

As for "Proof 2", I don't know what the "knot energy" means in this context. There is no indication what it could mean, except that it has exactly the right properties for the theorem (0 only for unknot and nonzero summands imply nonzero sum). It's really quite tautologous.

This is kind of a funny topic to have an article on. "Anti-knots" don't exist, so there really isn't a standard term for them. I doubt Crowell & Fox use the term, but I would have to check to be sure. There doesn't seem to be any worthwhile mathematical content here. Knot sum already mentions the theorem and mentions, for example, additivity of knot genus under knot sum can be used to prove it. The physics application seems to be a reference to Kelvin's vortex theory, but that was debunked long ago. What is left worth salvaging? I say take it to AFD, unless a good reason comes forth. --C S (Talk) 08:58, 20 March 2007 (UTC)[reply]

I'm a fairly strong inclusionist, and even I agree that this article is worthless. Unless the term is actually used in one of the references given (or another suitable reference), I would support deletion. (Alas, I have none of the references given.) The article Knot sum is the right place for this idea. (Actually, I just noticed that Knot sum redirects to Connected sum. Are they different enough to warrant separate articles?) Perhaps the section over there could be expanded a little bit to make it more than just a passing thought. VectorPosse 23:54, 20 March 2007 (UTC)[reply]