Connectivity properties of group actions on non-positively curved spaces I: Controlled connectivity and openness results
| dc.creator | Bieri, Robert | |
| dc.creator | Geoghegan, Ross | |
| dc.date | 1998-11-03 | |
| dc.date.accessioned | 2026-07-07T05:26:42Z | |
| dc.date.available | 2026-07-07T05:26:42Z | |
| dc.description | Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the space R := Hom(G, Isom(M)) with the compact open topology. Sample theorems: 1. The cocompact actions form an open subset of R. 2. The cocompact actions with discrete orbits whose point-stabilizers have type F_n form an open subset of the subspace of R consisting of all actions with discrete orbits. (F_1 means finitely generated, F_2 means finitely presented etc.) The key idea is to introduce a new "controlled topology" invariant of such actions - dependent on n - which is unfamiliar when the orbits are not discrete but which becomes familiar (cf 2.) when the orbits are discrete. (This is the first of two papers.) | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/9811007 | |
| dc.identifier | http://arxiv.org/abs/math/9811007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77646 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F32; 57N99 | |
| dc.title | Connectivity properties of group actions on non-positively curved spaces I: Controlled connectivity and openness results | |
| dc.type | text |