Geometric characterization of flat groups of automorphisms
| dc.creator | Baumgartner, Udo | |
| dc.creator | Schlichting, Günter | |
| dc.creator | Willis, George A. | |
| dc.date | 2008-07-31 | |
| dc.date.accessioned | 2026-07-07T09:54:00Z | |
| dc.date.available | 2026-07-07T09:54:00Z | |
| dc.description | If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In this note we prove the following partial converse: Assume that G is a totally disconnected, locally compact group such that B(G) is a proper metric space and let H be a group of automorphisms of G such that some (equivalently every) orbit of H in B(G) is quasi-isometric to n-dimensional euclidean space, then H has a finite index subgroup which is flat of rank n. We can draw this conclusion under weaker assumptions. We also single out a naturally defined flat subgroup of such groups of automorphisms. | |
| dc.description | 12 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/0807.5060 | |
| dc.identifier | http://arxiv.org/abs/0807.5060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166155 | |
| dc.subject | Group Theory | |
| dc.subject | 22D05 | |
| dc.title | Geometric characterization of flat groups of automorphisms | |
| dc.type | text |