Boundaries and JSJ decompositions of CAT(0)-groups
| dc.creator | Papasoglu, Panos | |
| dc.creator | Swenson, Eric | |
| dc.date | 2007-01-22 | |
| dc.date | 2008-12-01 | |
| dc.date.accessioned | 2026-07-07T12:16:58Z | |
| dc.date.available | 2026-07-07T12:16:58Z | |
| dc.description | Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of $G$ over two-ended groups and recover its JSJ decomposition from the boundary. We show that any discrete action of a group G on a CAT(0) space X satisfies a convergence type property. This is used in the proof of the results above but it is also of independent interest. In particular, if G acts co-compactly on X, then one obtains as a Corollary that if the Tits diameter of the boundary of X is bigger than $\frac {3π} 2$ then it is infinite and G contains a free subgroup of rank 2. | |
| dc.description | minor corrections,38 pages, 2 figures, to appear in GAFA | |
| dc.identifier | https://arxiv.org/abs/math/0701618 | |
| dc.identifier | http://arxiv.org/abs/math/0701618 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/211974 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | Metric Geometry | |
| dc.subject | 20F67,20E06,20E34,57M07 | |
| dc.title | Boundaries and JSJ decompositions of CAT(0)-groups | |
| dc.type | text |