Amenability of groups acting on trees
| dc.creator | Bartholdi, Laurent | |
| dc.date | 2002-04-07 | |
| dc.date | 2003-05-19 | |
| dc.date.accessioned | 2026-07-07T04:47:28Z | |
| dc.date.available | 2026-07-07T04:47:28Z | |
| dc.description | This note describes the first example of a group that is amenable, but cannot be obtained by subgroups, quotients, extensions and direct limits from the class of groups locally of subexponential growth. It has a balanced presentation \[Δ= < b,t|[b,t^2]b^{-1},[[[b,t^{-1}],b],b]>.\] I show that it acts transitively on a 3-regular tree, and that $Γ=< b,b^{t^{-1}}$ stabilizes a vertex and acts by restriction on a binary rooted tree. $Γ$ is a "fractal group", generated by a 3-state automaton, and is a discrete analogue of the monodromy action of iterates of f(z)=z^2-1 on associated coverings of the Riemann sphere. $Δ$ shares many properties with the Thompson group $F$. The proof of the main result (amenability of $Δ$) is incomplete in the present form; please refer to the paper arxiv.org/math.GR/0305262, joint with Balint Virag, for a complete proof. | |
| dc.description | 19 pages, 8 PostScript figures | |
| dc.identifier | https://arxiv.org/abs/math/0204076 | |
| dc.identifier | http://arxiv.org/abs/math/0204076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63730 | |
| dc.subject | Group Theory | |
| dc.subject | Functional Analysis | |
| dc.subject | 20E08, 43A07; 20F05, 20F65 | |
| dc.title | Amenability of groups acting on trees | |
| dc.type | text |