Talk:Thompson groups
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conjecture[edit]
Trying to trace the source of the statement about the Von Neumann conjecture.
Charles Matthews 06:33, 18 May 2004 (UTC)
Err - which statement? If you mean the statement that the conjecture has been disproved then I presume you've now found one as you've added details to the Von Neumann conjecture page. The statement that F, if proven not to be amenable, would be another counterexample, follows immediately from the fact that it doesn't contain a rank 2 free subgroup. The latter is well-known, but I can probably hunt out a reference if you think it needs one..... Best wishes, Cambyses 16:51, 18 May 2004 (UTC)
Yes, I later found a web reference to a f.p. counterexample. But maybe (I'm less clear) this wasn't the first counterexample to the vN conjecture . It seems there may have been some counterexample a fair few years ago.
Charles Matthews 17:19, 18 May 2004 (UTC)
We don't know[edit]
Please note that J. Moore no longer claims that F is amenable: http://arxiv.org/abs/1209.2063 "Over the weekend of September 29-30, 2012, Azer Akhmedov pointed out a serious error in Lemma 4.13. This error appears to be both serious and irreparable. I therefore withdraw my claim of a proof that F is amenable". T.K. — Preceding unsigned comment added by 2.100.216.103 (talk) 20:02, 2 January 2013 (UTC)
Explicit definition of these groups?[edit]
I'm a nonexpert in this area, but do the presentations and representations here suffice as a definition? It's a little unclear exactly what these groups are/how they're defined. Perhaps a definition section is fitting before the presentations section? Youarelovedfool (talk) 23:16, 8 May 2024 (UTC)
- Defining a group by a presentation is perfectly valid ; i added a link to the page on presentations of groups to make it more intelligible. The definitions via the action on the interval or circle are also perfectly fine (they may be detailed a bit more in the article). For these groups these definitions are likely to be as good as you can get since they are not representable by matrices. jraimbau (talk) 07:16, 9 May 2024 (UTC)