No-splitting property and boundaries of random groups

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 trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.

20 pages

References in corpus (2)

• Actions of finitely generated groups on R-trees
• Codimension one subgroups and boundaries of hyperbolic groups

Cited by in corpus (13)

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• Quasisymmetrically co-Hopfian Sierpiński Spaces and Menger Curve
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• Right-angled Coxeter groups with Menger curve boundary