Poisson boundary of groups acting on real trees

Abstract

We give a geometric description of the Poisson boundaries of certain extensions of free and hyperbolic groups. In particular, we get a full description of the Poisson boundaries of free-by-cyclic groups. We rely upon the description of Poisson boundaries by means of a topological compactification as developed by Kaimanovich. All the groups studied here share the property of admitting a sufficiently complicated action on some real tree.

42 pages. This is a majorly revised version. The introduction is completely rewritten, the statements are simplified. A new section entitled "The method" is added just after the introduction. More details are given on the case of a direct product of two finitely generated free groups

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• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
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