Combinatorial and group-theoretic compactifications of buildings
| dc.creator | Caprace, Pierre-Emmanuel | |
| dc.creator | Lecureux, Jean | |
| dc.date | 2009-01-27 | |
| dc.date.accessioned | 2026-07-07T12:34:49Z | |
| dc.date.available | 2026-07-07T12:34:49Z | |
| dc.description | Let X be a building of arbitrary type. A compactification $C_r(X)$ of the set Res(X) of spherical residues of X is introduced. We prove that it coincides with the horofunction compactification of Res(X) endowed with a natural combinatorial distance which we call the root-distance. Points of $C_r(X)$ admit amenable stabilisers in Aut(X) and conversely, any amenable subgroup virtually fixes a point in $C_r(X)$. In addition, it is shown that, provided Aut(X)is transitive enough, this compactification also coincides with the group-theoretic compactification constructed using the Chabauty topology on closed subgroups of Aut(X). This generalises to arbitrary buildings results established by Y. Guivarc'h and B. Rémy in the Bruhat--Tits case. | |
| dc.identifier | https://arxiv.org/abs/0901.4188 | |
| dc.identifier | http://arxiv.org/abs/0901.4188 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217573 | |
| dc.subject | Group Theory | |
| dc.subject | 20E42; 20G25, 22E20, 22F50, 51E24 | |
| dc.title | Combinatorial and group-theoretic compactifications of buildings | |
| dc.type | text |