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We obtain a description of Poisson–Furstenberg boundaries for (random walks on) fundamental groups of compact graph-manifolds. Together with previously known results due to V.A. Kaimanovich and others, this allows one to obtain descriptions of Poisson–Furstenberg boundaries for fundamental groups of all closed 3-manifolds.

生成讲解博客的中文版本

生成AI智能校验的中文版本