May 5th, 2007, 5:09 am
QuoteOriginally posted by: NHere's an excerpt describing the Poincare conjecture,"Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere".The problem is that smooth three-manifolds (octonions) have only a single point projection onto a Euclidean space (the space of the three-sphere)! That's basically the same as saying Fermions have only position and momentum, all the other dimensions are orthogonal/rolled up. BTW, simply connected doesn't mean there are no knots (since there are tons of knots in octonions), but it does mean all the knots must unwind at the single point in Euclidean space.Unfortunately, there is no way to be homeomorphic to a single point. So I's say the Poincare conjecture is neither right or wrong, it's just a stupid question.Hm, first of all it's a manifold so by definition it has a set of maps, where the manifold is covered by all the maps and each map has a homeomorphism onto an open set of euclidian space(basically it's a disco). So how is it a single-point projection?And three-sphere isn't Euclidean Space because you can't enter the local coordinates with the help of one map(e.g. north and south poles have problem) so three-sphere isn't homeomorphic to Euclidean space. I don't get your argument...