Timeline for What makes the amenability of Thompsons group $F$ such a tricky problem?
Current License: CC BY-SA 3.0
17 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jun 16, 2015 at 8:46 | comment | added | Matt Brin | In my opinion, the question posed by Tobias has replaced the amenability question as the main question of interest. A solution of the original problem that fails to show where the difficulty lay would be quite disappointing. | |
| Nov 25, 2014 at 9:54 | comment | added | ARG | There is some "numerical evidence" (that is to say no evidence at all) that Thomson's group is non-amenable: see arxiv.org/abs/1312.5722 | |
| Nov 20, 2014 at 3:04 | review | Close votes | |||
| Nov 20, 2014 at 11:17 | |||||
| Nov 14, 2014 at 22:39 | history | edited | Tobias Kildetoft | CC BY-SA 3.0 |
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| Nov 13, 2014 at 16:54 | answer | added | Timothy Chow | timeline score: 16 | |
| Nov 13, 2014 at 14:54 | comment | added | Benjamin Steinberg | Many famous open problems probably have some consensus as to which way the answer lies. My feeling is the experts are 50-50 on this one. | |
| Nov 13, 2014 at 14:01 | comment | added | Benjamin Steinberg | One reason might be that there are some numerical quantities that imply amenability of a group and some of the experimental approximations of these quantities for F seem to hang right near the border. | |
| Nov 13, 2014 at 13:32 | comment | added | Yemon Choi | @QiaochuYuan By way of comparison, one doesn't see at least two people announce proofs that all free group factors are distinct while two more announce proofs that they are all isomorphic | |
| Nov 13, 2014 at 13:01 | comment | added | Todd Trimble | See also: meta.mathoverflow.net/questions/1971/… | |
| Nov 13, 2014 at 10:24 | review | Close votes | |||
| Nov 13, 2014 at 13:32 | |||||
| Nov 13, 2014 at 9:04 | comment | added | Tobias Kildetoft | @QiaochuYuan But mathematicians thinking they have solved a (quite wellknown) open problem for long enough to actually announce the proof is a fairly rare occurrence, so given the large number of such problems, it seems that it should not take that many to be an unlikely outlier. | |
| Nov 13, 2014 at 8:48 | comment | added | Qiaochu Yuan | I mean consider a random model where each mathematician believes they have solved a random open problem with some probability. It is moderately likely that some open problem, by chance, has the property that somewhat more mathematicians believe they have solved it than other problems. That isn't strong evidence that the problem is particularly special. | |
| Nov 13, 2014 at 8:47 | comment | added | Andreas Thom | I do not think that there is a good answer to this question. What kind of answer are you looking for? How to measure the difficulty of an open problem if not in terms of failed attempts? Maybe one reason for the number of attempts is that the problem is elementary to state, but I wouldn't call this "inherent to the problem". | |
| Nov 13, 2014 at 8:42 | comment | added | Tobias Kildetoft | @QiaochuYuan I am not sure I understand what you mean by "what problems people think they have solved". What problems do you mean? | |
| Nov 13, 2014 at 8:35 | comment | added | Qiaochu Yuan | The sample size seems pretty small here. Nothing that can't be explained by random variation in what problems people think they've solved. | |
| Nov 13, 2014 at 8:20 | history | asked | Tobias Kildetoft | CC BY-SA 3.0 |