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Boundaries of right-angled hyperbolic buildings. (English) Zbl 1177.20042

Summary: We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

MSC:

20E42 Groups with a \(BN\)-pair; buildings
20F67 Hyperbolic groups and nonpositively curved groups
57M07 Topological methods in group theory
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