Timeline for Examples of results first proved using geometrical methods?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2021 at 14:53 | history | edited | Sam Hopkins |
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| Sep 12, 2021 at 14:26 | history | edited | Stefan Kohl♦ |
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| Sep 4, 2011 at 19:27 | answer | added | HJRW | timeline score: 1 | |
| Sep 4, 2011 at 19:23 | comment | added | HJRW | ... Almost by definition, any 'simple' results can be proved without reference to geometry. | |
| Sep 4, 2011 at 19:22 | answer | added | HJRW | timeline score: 2 | |
| Sep 4, 2011 at 19:20 | comment | added | HJRW | I think the OP needs to tell is whether or not the covering-spaces-of-graphs proof that a subgroup of a free group is free is the sort of thing that she is looking for. It's a great example of the power of geometric thinking for an elementary introduction, but as Ryan observes it's not a result that was by any means inaccessible beforehand. | |
| Sep 4, 2011 at 17:37 | answer | added | Ian Agol | timeline score: 2 | |
| Sep 4, 2011 at 17:18 | answer | added | Benjamin Steinberg | timeline score: 4 | |
| Sep 4, 2011 at 5:18 | history | edited | user15626 | CC BY-SA 3.0 |
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| Sep 4, 2011 at 4:46 | comment | added | Yemon Choi | (On 2nd thoughts I am being a bit uncharitable. Nevertheless, I second Ryan's suggestion/request for a more focused question. Maybe something on Bass-Serre theory?) | |
| Sep 4, 2011 at 4:45 | comment | added | Yemon Choi | Perhaps I have misunderstood the question, but it seems to veer uncomfortably close to "please write an enyclopaedia entry for me", which I thought we had decided was not MO's metier | |
| Sep 4, 2011 at 4:33 | history | made wiki | Post Made Community Wiki by user15626 | ||
| Sep 4, 2011 at 3:56 | comment | added | Ryan Budney | @Birdman, if you're thinking about the covering space argument, that specific proof technically predates geometric group theory. Moreover, there were earlier (essentially equivalent) proofs that predated covering space arguments, so such an argument certainly wasn't "inacessible" before geometric group theory. | |
| Sep 4, 2011 at 3:49 | comment | added | Spice the Bird | What about the subgroup of a free group is free. | |
| Sep 4, 2011 at 3:30 | comment | added | Ryan Budney | This should be Community Wiki (you'll have to edit your post to make this change) as there's no "right" answer. Also, your question is a little vague, in that you're basically asking people to tell you about geometric group theory. Could you narrow it down a bit? For example, the Wikipedia "Geometric Group Theory" page must partially answer your question -- if so, what else are you looking for? | |
| Sep 4, 2011 at 3:25 | history | asked | user15626 | CC BY-SA 3.0 |