Timeline for Poincaré Conjecture and the Shape of the Universe

Current License: CC BY-SA 2.5

5 events

when toggle format	what		by	license	comment
Dec 27, 2009 at 0:52	comment	added	José Figueroa-O'Farrill		The answer might indeed well be "no". My point is simply that the topology of the universe is not "a matter of opinion", since it can be tested empirically.
Dec 27, 2009 at 0:19	comment	added	Pete L. Clark		I had a thought which Ian Agol's answer confirmed: if you're already assuming that your manifold is a space-form, what do you need the Poincare Conjecture for? Thus I think again that the answer to the poster's precise question has got to be "no".
Dec 25, 2009 at 8:44	comment	added	José Figueroa-O'Farrill		That the large scale structure of the spatial universe looks like a space form follows from two properties: isotropy and homogeneity. Isotropy is something that can be empirically tested. Penzias and Wilson measured the cosmic microwave background and noticed that it is isotropic to a large degree. I think that temperature fluctuations (divided by temperature) are of the order of $10^{-4}$ or thereabouts. Homogeneity, on the other hand, is an assumption: usually paraphrased as the principle of mediocrity. As usual, at the end it's always Occam's razor.
Dec 25, 2009 at 7:58	comment	added	Pete L. Clark		Again, I think my use of "risible" was not interpreted as I had intended; I edited my post in an attempt at clarification. To me, Gromov's remark (as reported by Krantz; the title of his book contains, after all, the word apocrypha) emphasizes that a lot of assumptions have to be made in order for the question of simply connectedness of the universe to make good sense. (For instance, why is it reasonable to assume that the universe, as a Riemannian manifold, is a space form?) I don't wish to deny that there is deep and interesting mathematics and physics here.
Dec 25, 2009 at 1:18	history	answered	José Figueroa-O'Farrill	CC BY-SA 2.5