Contractible groups and linear dilatation structures
| dc.creator | Buliga, Marius | |
| dc.date | 2007-05-10 | |
| dc.date | 2007-06-06 | |
| dc.date.accessioned | 2026-07-07T08:04:06Z | |
| dc.date.available | 2026-07-07T08:04:06Z | |
| dc.description | A dilatation structure on a metric space, arXiv:math/0608536v4, is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. Linearity is also a property which can be explained with the help of a dilatation structure. In this paper we show that we can speak about two kinds of linearity: the linearity of a function between two dilatation structures and the linearity of the dilatation structure itself. Our main result here is a characterization of contractible groups in terms of dilatation structures. To a normed conical group (normed contractible group) we can naturally associate a linear dilatation structure. Conversely, any linear and strong dilatation structure comes from the dilatation structure of a normed contractible group. | |
| dc.description | larger, updated version | |
| dc.identifier | https://arxiv.org/abs/0705.1440 | |
| dc.identifier | http://arxiv.org/abs/0705.1440 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129829 | |
| dc.subject | Group Theory | |
| dc.subject | Metric Geometry | |
| dc.subject | 22E20; 20E36; 20F65; 22A10; 51F99 | |
| dc.title | Contractible groups and linear dilatation structures | |
| dc.type | text |