Timeline for The Hopf invariant is an isomorphism for $\pi_3 (S^2)$
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2018 at 22:28 | history | edited | j.c. | CC BY-SA 3.0 |
fix grammar
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| Mar 16, 2018 at 14:40 | answer | added | Piotr Hajlasz | timeline score: 7 | |
| Apr 28, 2017 at 8:38 | vote | accept | Jean Van Schaftingen | ||
| Apr 26, 2017 at 20:47 | comment | added | Denis T | If you are interested in more general question of describing homotopy category of simply connected $n$-complexes, where $n$ is not very large, you can look at H.-J. Baues works and particularly his book "Homotopy type and homology", where he introduces purely algebraic method of doing it. For example, $\pi_3(X) = \Gamma(\pi_2(X))$, which is slight extension of Hopf invariant case, can be proven uniformly for all simply connected complexes with vanishing 3 and 4 integral homology. | |
| Apr 25, 2017 at 10:39 | answer | added | Ronnie Brown | timeline score: 0 | |
| Apr 25, 2017 at 5:42 | comment | added | Thomas Rot | Isn't this in pontryagin's book? | |
| Apr 25, 2017 at 5:19 | answer | added | Jeff Strom | timeline score: 2 | |
| Apr 25, 2017 at 0:17 | answer | added | Andy Putman | timeline score: 11 | |
| Apr 24, 2017 at 23:57 | answer | added | Nicholas Kuhn | timeline score: 9 | |
| Apr 24, 2017 at 14:30 | comment | added | Robert Bryant | Doesn't this follow immediately from the long exact sequence in homotopy for a fibration? (Apply it to the Hopf fibration $\pi:S^3\to S^2$ with fiber $S^1$.) If so, there would certainly be a proof in Steenrod's The topology of fibre bundles. | |
| Apr 24, 2017 at 14:22 | history | asked | Jean Van Schaftingen | CC BY-SA 3.0 |