Timeline for "Why the heck are the homotopy groups of the sphere so damn complicated?"
Current License: CC BY-SA 4.0
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| Sep 20, 2018 at 16:56 | comment | added | Noah Snyder | I think this gets it exactly right. Before you learn about the Hopf map it's quite reasonable to think that homotopy groups of spheres might be easy (after all, $\pi_k(S^n)$ for $k \leq n$ is easy), but once you learn about the Hopf map your intuition should switch "if we have this construction why shouldn't there be zillions of other similar constructions"? (This is especially true if you think of the Hopf map as coming from the Eckman-Hilton argument a la Pontryagin rather than as involving a division algebra argument.) | |
| S Sep 18, 2018 at 17:01 | history | answered | Timothy Chow | CC BY-SA 4.0 | |
| S Sep 18, 2018 at 17:01 | history | made wiki | Post Made Community Wiki by Timothy Chow |