Covering R-trees, R-free groups, and dendrites
| dc.creator | Berestovskii, V. N. | |
| dc.creator | Plaut, C. P. | |
| dc.date | 2009-04-23 | |
| dc.date.accessioned | 2026-07-07T13:08:23Z | |
| dc.date.available | 2026-07-07T13:08:23Z | |
| dc.description | We prove that every length space X is the orbit space (with the quotient metric) of an R-tree T via a free action of a locally free subgroup G(X) of isometries of X. The mapping f:T->X is a kind of generalized covering map called a URL-map and is universal among URL-maps onto X. T is the unique R-tree admitting a URL-map onto X. When X is a complete Riemannian manifold M of dimension n>1, the Menger sponge, the Sierpin'ski carpet or gasket, T is isometric to the so-called "universal" R-tree A_{c}, which has valency equal to the cardinality of the continuum at each point. In these cases, and when X is the Hawaiian earring H, the action of G(X) on T gives examples in addition to those of Dunwoody and Zastrow that negatively answer a question of J. W. Morgan about group actions on R-trees. Indeed, for one length metric on H, we obtain precisely Zastrow's example. | |
| dc.description | This paper is the result of splitting off some of the results in the preprint "Covering R-trees" and adding additional applications to R-free groups | |
| dc.identifier | https://arxiv.org/abs/0904.3767 | |
| dc.identifier | http://arxiv.org/abs/0904.3767 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228404 | |
| dc.subject | Metric Geometry | |
| dc.subject | General Topology | |
| dc.subject | 57M07; 20F65, 28A80, 53C23, 54F15, 54F50 | |
| dc.title | Covering R-trees, R-free groups, and dendrites | |
| dc.type | text |