Timeline for What makes the amenability of Thompsons group $F$ such a tricky problem?
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| Nov 19, 2014 at 1:31 | comment | added | Yemon Choi | @DavidLHarden Also, see this from Tobias's question: "some aspect that makes so many serious mathematicians convince themselves that they have a solution, and so many other serious mathematicians to take so long to find the errors?" | |
| Nov 19, 2014 at 1:29 | comment | added | Yemon Choi | @DavidLHarden I am not sure I agree with your comment. The key feature of the problem for Thompson F is that people have made serious claims for and against its amenability. This distinguishes it from problems like Jacobian conjecture, Collatz, RH etc where most failed attempts seek a positive answer | |
| Nov 18, 2014 at 23:37 | comment | added | DavidLHarden | The amenability of Thompson's group does not appear to be an isolated instance of this. The complexity of graph isomorphism is somewhat similar, and led the author of this paper to use the term "disease": onlinelibrary.wiley.com/doi/10.1002/jgt.3190010410/pdf So now write 'The Thompson Group Amenability Disease' or something like that? And maybe 'The Jacobian Conjecture Disease' while we're at it? What other examples of 'diseases' are out there? | |
| Nov 14, 2014 at 14:15 | comment | added | Yemon Choi | I started to write a vague answer but deleted it. The gist of it was as follows: there seem to be two worlds, the "obviously amenable" and the "obviously non-amenable", and many examples one thinks of fall into these classes. Thompson's F belongs to neither. So we have easily applicable sufficient conditions and easily applicable necessary conditions but a big gap in between, and Thompson's F is somehow one of a small number of explicitly described groups that lie in the gap. What I don't know is how it differs from groups in the gap which are nevertheless known to be amenable or non-amenable. | |
| Nov 13, 2014 at 17:32 | comment | added | Benjamin Steinberg | Also amenability has a vast number of equivalent formulations, not all so trivial to prove which leads to many avenues of attack. | |
| Nov 13, 2014 at 16:54 | history | answered | Timothy Chow | CC BY-SA 3.0 |