Timeline for Properties (T) and (FA)
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 21, 2021 at 16:24 | comment | added | HJRW | @guest5781 cites a paper of Dahmani--Guirardel--Przytycki, who proved that random groups in the Gromov density model have property (FA) at all positive densities. By way of contrast, (T) is known to hold at density greater than 1/3 (by a theorem of Zuk--Kotowski--Kotowski), and known not to hold at densities <5/24 (by a theorem of Mackay--Przytycki). So groups random groups at densities <5/24 also provide examples. | |
| May 21, 2021 at 9:21 | history | became hot network question | |||
| May 21, 2021 at 9:11 | comment | added | HJRW | Some of the most classical examples that illustrate the difference are the fundamental groups of non-Haken 3-manifolds. These have Property (FA), but never (T). | |
| May 21, 2021 at 5:33 | answer | added | AGenevois | timeline score: 8 | |
| May 21, 2021 at 5:09 | comment | added | AGenevois | Many groups acting non-trivially on CAT(0) cube complexes (in particular, they do not have (T)) have (FA). See for instance: mathoverflow.net/questions/308865/… | |
| May 21, 2021 at 3:50 | comment | added | Venkataramana | The wikipedia article has quite a bit of information about groups with property FA but not property T. For example $SL_2({\mathbb Z}[{\sqrt 2}])$ has property FA but not property T. en.wikipedia.org/wiki/Serre%27s_property_FA | |
| May 21, 2021 at 1:26 | comment | added | guest5781 | You should look at the random groups in the Gromov density model and see if the density for (FA) is not the same as for (T). See this paper. | |
| May 21, 2021 at 1:25 | review | First posts | |||
| May 21, 2021 at 5:56 | |||||
| May 21, 2021 at 1:19 | history | asked | NoName | CC BY-SA 4.0 |