Timeline for "Why the heck are the homotopy groups of the sphere so damn complicated?"
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2018 at 17:01 | answer | added | Timothy Chow | timeline score: 13 | |
| May 16, 2017 at 16:40 | answer | added | Neil Strickland | timeline score: 9 | |
| May 16, 2017 at 14:44 | answer | added | Stephan Zhechev | timeline score: 9 | |
| Feb 15, 2012 at 1:46 | comment | added | Spice the Bird | One reason could be is that the category of finite sets, and the symmetric groups are complicated. See question mathoverflow.net/questions/76541 | |
| Apr 29, 2010 at 2:22 | comment | added | Matt | Sorry, I swear I heard Doug Ravenel say that his (with Mike Hill and Mike Hopkins) result about the Kervaire Invariant problem implied the Doomsday conjecture. I guess it was just "a Doomsday-type conjecture"? | |
| Apr 28, 2010 at 9:30 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
edited to improve anonymity and remove unacademic language
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| Apr 28, 2010 at 7:31 | history | edited | The Mathemagician | CC BY-SA 2.5 |
Removed my friend's name by his request.
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| Apr 27, 2010 at 12:57 | comment | added | Tyler Lawson | @hilbertthm90: As Charles posted, the original Doomsday conjecture was proven false by Mahowald in ~1971. The homotopy groups of spheres have been computable through a range since Serre's work on spectral sequences and have resisted most attempts to find simple systematic patterns ever since. | |
| Apr 27, 2010 at 8:39 | answer | added | Lennart Meier | timeline score: 27 | |
| Apr 27, 2010 at 8:08 | comment | added | Martin Brandenburg | I think the question needs extra explanation. calculations show that the homotopy groups are complicated, well, but this is not the answer, right? perhaps you are looking for an empirical argument that spheres have nontrivial higher homotopy groups? | |
| Apr 27, 2010 at 6:59 | answer | added | Andrew Stacey | timeline score: 42 | |
| Apr 27, 2010 at 6:41 | answer | added | Dev Sinha | timeline score: 33 | |
| Apr 27, 2010 at 6:35 | comment | added | Qiaochu Yuan | I think mathematical objects should be complicated until proven simple. | |
| Apr 27, 2010 at 6:34 | comment | added | Charles Siegel | @hilbertthm90, perhaps this will help with the Doomsday Conjecture and it's relationship to spheres: books.google.com/… I can't say that I understand it, but it seems relevant. | |
| Apr 27, 2010 at 6:26 | comment | added | Matt | I've been told that it was only conjectured that they are complicated. It wasn't until the "Doomsday Conjecture" was proved (except one case) in the past year that we knew for a fact that it was hopeless for us to ever get a grip on them. I have absolutely no idea what the Doomsday Conjecture says or how it relates, this is just what I've heard. | |
| Apr 27, 2010 at 6:21 | history | asked | The Mathemagician | CC BY-SA 2.5 |