Timeline for Is Thompson's Group F amenable?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2014 at 12:37 | comment | added | Mariarty | Another try from Poland arxiv.org/pdf/1408.2188.pdf | |
| Nov 16, 2013 at 17:20 | comment | added | Mariarty | If someone has examined Akhmedov's previous paper, can you please clear is this paper (arxiv.org/pdf/1310.4395.pdf) a fixed one or is it a new one? | |
| Nov 25, 2012 at 11:10 | history | edited | Mariarty | CC BY-SA 3.0 |
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| Oct 3, 2012 at 4:53 | comment | added | Yemon Choi | Thank you for the clarification. If the proof is successfully validated then I will be as interested and delighted as anyone. | |
| Oct 2, 2012 at 21:09 | comment | added | Mariarty | @Yemon Choi, you are absolutely right about overconfidence of my statement. It was an emotional impulse because Prof. Levon Beklaryan is my father and the problem of the classification theorem for groups of homeomorphisms of the line waited for the solutions for 20 years. I didn't edit my post because I thought that it would be unethical towards the participants of the community. My name is Armen and I am PhD in MSU and specialize in differential equations. | |
| Oct 2, 2012 at 19:42 | comment | added | Yemon Choi | @Mariarty, could you please clarify your relationship to Beklaryan? It feels strange to have someone using a pseudonym but making such strong claims about someone's claim to have solved a notorious problem. | |
| Oct 2, 2012 at 14:47 | comment | added | Mariarty | There an error has been found in the proof of Lemma 4.13 in Justin T. Moore's paper. Maybe author will repair the proof, but despite active minuses against my post immediately after his announcement of amenability, I still believe in the proof of NONamenability from my post. Pointed paper will soon be updated with the simplification of the proof. | |
| Oct 2, 2012 at 8:21 | comment | added | Lior Silberman | Unfortunately, Moore has just withdrawn this preprint. | |
| Jun 12, 2012 at 6:16 | comment | added | Mariarty | There is update of the paper arxiv.org/abs/1112.1942 | |
| Apr 12, 2012 at 20:42 | comment | added | Olga | I'm sorry for the impatience - but did anything change in these 4 months? That's a theme of a great interest! | |
| Jan 7, 2012 at 15:09 | comment | added | Matt Brin | The main result of the preprint in question claims that if G is an amenable group acting by orientation preserving homeomorphisms on R, then there is a "projectively G-invariant" measure on R (action of any element on the measure only dilates the measure). There is a counterexample to this with a group in which every element has a fixed point. The author says that adding a hypothesis that G has at least one fixed point free element will fix the theorem (and still apply to F). Details were promised. We will have to wait and see. | |
| Dec 16, 2011 at 12:16 | comment | added | Mariarty | Yes, I have. I think next week there will be corrected version in arXiv. | |
| Dec 16, 2011 at 5:15 | comment | added | Yemon Choi | "The author has already engaged in a reformulation of the text" - do you mean you have spoken to him? | |
| Dec 15, 2011 at 21:15 | comment | added | Mariarty | There is a small inaccuracy in the statement of Theorem A: condition of non-emptiness of the minimal set should be replaced by the stronger condition of existence of a freely acting element. After that such subgroups of $F$, which have non-empty minimal set, but don't have a freely acting element, can't be applied to Theorem A. The author has already engaged in a reformulation of the text. | |
| Dec 15, 2011 at 16:35 | comment | added | user6976 | Matt Brin has found a problem in the text already and is discussing it with the author. The problem, as far as I understand, is that the method used in the paper can also "prove" that some clearly amenable subgroups of $F$ are non-amenable. | |
| Dec 9, 2011 at 10:40 | comment | added | Mariarty | Indeed, the minimal set of this subgroup seems to coincide with R, so it's trivial subgroup. So which case do you mean? | |
| Dec 9, 2011 at 2:07 | comment | added | Yemon Choi | More pointedly, skimming through the paper, it claims to show that the quotient of $F$ by some canonical normal subgroup $H_F$ is non-amenable. But then since the commutator subgroup of $F$ is simple, this would force $H_F$ to be trivial, and it seems unclear why that should be the case... | |
| Dec 9, 2011 at 1:35 | comment | added | Yemon Choi | I think we should wait for closer examination of the paper before saying that the problem is definitely solved. | |
| Dec 9, 2011 at 1:18 | history | answered | Mariarty | CC BY-SA 3.0 |