Connectivity properties of group actions on non-positively curved spaces II: The geometric invariants
| 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 | This is the second of two papers but has been written so as to have minimal dependence on the first paper (which is also on this archive). 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). Assume G is of type F_n (type F_1 is finitely generated, type F_2 is finitely presented etc.) The "boundary", bdM, of M at infinity has two customary topologies - the compact "cone" topology and the Tits metric topology. We associate with any isometric action of G on M two subsets of bdM, both dependent on n. These subsets consist of those points of bdM at which - in two senses - the action is "controlled (n-1)-connected". One of these sets is open in the Tits metric topology. Even in classical cases like familiar groups of isometries of the hyperbolic plane or of a locally finite tree these sets seem to be new and interesting invariants. The "SIGMA-theory" of Bieri-Neumann-Strebel-Renz is recovered in the special case in which M is G(abelianized) tensor R with the translation action. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/9811008 | |
| dc.identifier | http://arxiv.org/abs/math/9811008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77647 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F32; 57N99 | |
| dc.title | Connectivity properties of group actions on non-positively curved spaces II: The geometric invariants | |
| dc.type | text |