Timeline for Parallelizability of the Milnor's exotic spheres in dimension 7
Current License: CC BY-SA 2.5
4 events
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| Aug 26, 2015 at 19:46 | comment | added | Allen Hatcher | The stable parallelizability of exotic spheres is Theorem 3.1 of the famous Kervaire-Milnor paper "Groups of homotopy spheres I" in the 1963 Annals. The proof is short but uses several big theorems from the previous decade such as Bott periodicity, the Hirzebruch signature theorem, and Adams' work on the J-homomorphism. | |
| Aug 23, 2015 at 20:56 | comment | added | Ali Taghavi | @AllenHatcher I am sorry if my question is elementary: Why exotic spheres are stably parallelizable)? | |
| Jul 28, 2013 at 15:22 | comment | added | András Szűcs | This Bredon Kosinski theorem can be deduced from Smale-Hirsch immersion theory. (May be BK did this way, I do not know.) So immersion theory implies that a stably parallelizable manifold immerses into Euclidean space with codimension one. Then using the Gauss map one can pull back the vectorfields on the sphere to the immersed manifold. Hence a stably parallelizable manifold admits at least as many vector fields as the sphere of the same dimension. | |
| Mar 11, 2011 at 17:45 | history | answered | Allen Hatcher | CC BY-SA 2.5 |