Polygonal \(\mathcal{VH}\) complexes. (English) Zbl 1286.20056

Summary: Ian Leary inquires whether a class of hyperbolic finitely presented groups are residually finite. We answer in the affirmative by giving a systematic version of a construction in his paper, which shows that the standard 2-complexes of these presentations have a \(\mathcal{VH}\)-structure. This structure induces a splitting of these groups, which together with hyperbolicity, implies that these groups are residually finite.


20F67 Hyperbolic groups and nonpositively curved groups
20E26 Residual properties and generalizations; residually finite groups
57M07 Topological methods in group theory
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