Hausdorff dimension of some groups acting on the binary tree
| dc.creator | Siegenthaler, Olivier | |
| dc.date | 2006-09-08 | |
| dc.date | 2007-10-01 | |
| dc.date.accessioned | 2026-07-07T10:00:44Z | |
| dc.date.available | 2026-07-07T10:00:44Z | |
| dc.description | Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T. Abert and Virag showed that there exist finitely generated (but not necessarily level-transitive) subgroups of AutT of arbitrary dimension in [0,1]. In this article we explicitly compute the Hausdorff dimension of the level-transitive spinal groups. We then show examples of 3-generated spinal groups which have transcendental Hausdroff dimension, and exhibit a construction of 2-generated groups whose Hausdorff dimension is 1. | |
| dc.description | 10 pages; full revision; simplified some proofs | |
| dc.identifier | https://arxiv.org/abs/math/0609237 | |
| dc.identifier | http://arxiv.org/abs/math/0609237 | |
| dc.identifier | Journal of Group Theory (2008), Vol. 11 (4), p. 555-567 | |
| dc.identifier | doi:10.1515/JGT.2008.034 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168404 | |
| dc.subject | Group Theory | |
| dc.subject | 20E08 (Primary); 28A78 (Secondary) | |
| dc.title | Hausdorff dimension of some groups acting on the binary tree | |
| dc.type | text |