Abstract
We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on simplicial trees. This implies that their Gromov boundaries, defined at density less than \({\frac{1}{2}}\) , are Menger curves.
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F. Dahmani and V. Guirardel were partially supported by ANR Grant ANR–06-JCJC-0099-01. P. Przytycki was partially supported by MNiSW Grant N201 012 32/0718, the Foundation for Polish Science, and ANR Grant ZR58.
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Dahmani, F., Guirardel, V. & Przytycki, P. Random groups do not split. Math. Ann. 349, 657–673 (2011). https://doi.org/10.1007/s00208-010-0532-4
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DOI: https://doi.org/10.1007/s00208-010-0532-4