Just-infinite branch pro-p groups introduced earlier by the author are shown to be rigid on trees obtained by deleting levels, forcing every branch action on the p-adic tree to be zero-dimensional and disproving Boston's conjecture.
The Hausdorff dimension of the generalized Brunner-Sidki-Vieira Groups
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abstract
We compute the Hausdorff dimension of the closure of the generalized Brunner-Sidki-Vieira group acting on the $m$-adic tree for $m\ge 2$, providing the first examples of self-similar topologically finitely generated closed subgroups of transcendental Hausdorff dimension in the group of $m$-adic automorphisms.
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Weakly branch actions: first-order theory, rigidity and Boston's conjecture
Just-infinite branch pro-p groups introduced earlier by the author are shown to be rigid on trees obtained by deleting levels, forcing every branch action on the p-adic tree to be zero-dimensional and disproving Boston's conjecture.