Cocompact Proper CAT(0) Spaces
| dc.creator | Geoghegan, Ross | |
| dc.creator | Ontaneda, Pedro | |
| dc.date | 2004-07-29 | |
| dc.date.accessioned | 2026-07-07T05:10:49Z | |
| dc.date.available | 2026-07-07T05:10:49Z | |
| dc.description | This paper is about geometric and topological properties of a proper CAT(0) space $X$ which is cocompact - i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in $X$ can "almost" be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem that there is a top dimension $d$ in which the compactly supported integral cohomology of $X$ is non-zero. It is also proved that the boundary-at-infinity of $X$ (with the cone topology) has Lebesgue covering dimension $d-1$. It is not assumed that there is any cocompact discrete subgroup of the isometry group of $X$; however, a corollary for that case is that "the dimension of the boundary" is a quasi- isometry invariant of CAT(0) groups. (By contrast, it is known that the topological type of the boundary is not unique for a CAT(0) group.) | |
| dc.identifier | https://arxiv.org/abs/math/0407506 | |
| dc.identifier | http://arxiv.org/abs/math/0407506 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72049 | |
| dc.subject | Metric Geometry | |
| dc.subject | Algebraic Topology | |
| dc.title | Cocompact Proper CAT(0) Spaces | |
| dc.type | text |