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Hausdorff dimension of some groups acting on the binary tree

Olivier Siegenthaler
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Abstract

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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Olivier Siegenthaler. 2007-10-01. Hausdorff dimension of some groups acting on the binary tree. https://doi.org/10.1515/jgt.2008.034

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