The Action of Thompson's Group on a CAT(0) Boundary
| dc.creator | Farley, Daniel | |
| dc.date | 2006-04-04 | |
| dc.date.accessioned | 2026-07-07T07:10:30Z | |
| dc.date.available | 2026-07-07T07:10:30Z | |
| dc.description | One way to show that Thompson's group F is non-amenable is to exhibit an action of F on a locally compact CAT(0) space X containing no F-invariant flats and having no global fixed points in its boundary-at-infinity. We study the actions of Thompson's groups F, T, and V on the boundaries-at-infinity of proper CAT(0) cubical complexes. In particular, we show that Thompson's groups T and V act without fixing any points in the boundaries of their CAT(0) cubical complexes. This in particular gives another proof of the well-known fact that these groups are non-amenable. We obtain a partial description of the fixed set for F: Thompson's group F fixes an arc in the boundary of its cubical complex. We leave open the possibility that there are more fixed points, but describe a region of the boundary which must contain all of the others. | |
| dc.description | 33 pages, 28 figures | |
| dc.identifier | https://arxiv.org/abs/math/0604077 | |
| dc.identifier | http://arxiv.org/abs/math/0604077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111442 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 20F69 | |
| dc.title | The Action of Thompson's Group on a CAT(0) Boundary | |
| dc.type | text |