Hausdorff dimension of some groups acting on the binary tree

Details Hausdorff dimension of some groups acting on the binary tree Hausdorff dimension of some groups acting on the binary tree

2006-09-08

arxiv.org/abs/math/0609237v4

Journal of Group Theory (2008), Vol. 11 (4), p. 555-567

Mathematics

Group Theory

10 pages; full revision; simplified some proofs

Scientific paper

10.1515/JGT.2008.034

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.

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