Polák, Jason K. C.; Wise, Daniel T. Polygonal \(\mathcal{VH}\) complexes. (English) Zbl 1286.20056 Publ. Mat., Barc. 57, No. 2, 421-428 (2013). 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. MSC: 20F67 Hyperbolic groups and nonpositively curved groups 20E26 Residual properties and generalizations; residually finite groups 57M07 Topological methods in group theory Keywords:residually finite groups; hyperbolic groups; nonpositively curved cube complexes PDF BibTeX XML Cite \textit{J. K. C. Polák} and \textit{D. T. Wise}, Publ. Mat., Barc. 57, No. 2, 421--428 (2013; Zbl 1286.20056) Full Text: DOI arXiv Euclid OpenURL References: [1] M. R. Bridson, On the existence of flat planes in spaces of nonpositive curvature, Proc. Amer. Math. Soc. 123(1) (1995), 223\Ndash235. \smallDOI: 10.2307/2160630. · Zbl 0840.53033 [2] S. M. Gersten and H. Short, Small cancellation theory and automatic groups: Part II, Invent. Math. 105(3) (1991), 641\Ndash662. \smallDOI: 10.1007/BF01232283. · Zbl 0734.20014 [3] I. J. Leary, A metric Kan-Thurston theorem, Preprint. \small\texttt · Zbl 1343.20044 [4] D. T. Wise, The structure of groups with a quasiconvex hierar-chy, submitted. Available at: \smallhttp://www.math.mcgill.ca/wise/ \smallpapers. [5] D. T. Wise, Subgroup separability of the figure 8 knot group, Topology 45(3) (2006), 421\Ndash463. \smallDOI: 10.1016/j.top.2005.06. \small004. · Zbl 1097.20030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.