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On asymptotically hereditarily aspherical groups. (English) Zbl 1360.20040
Summary: We undertake a systematic study of asymptotically hereditarily aspherical (AHA) groups, the class of groups introduced by T. Januszkiewicz and the second author [Publ. Math., Inst. Hautes Étud. Sci. 104, 1–85 (2006; Zbl 1143.53039)] as a tool for exhibiting exotic properties of systolic groups. We provide many new examples of AHA groups, also in high dimensions. We relate the AHA property with the topology at infinity of a group, and deduce in this way some new properties of (weakly) systolic groups. We also exhibit an interesting property of boundaries at infinity for a few classes of AHA groups.

##### MSC:
 20F69 Asymptotic properties of groups 20F65 Geometric group theory 20J05 Homological methods in group theory 20F67 Hyperbolic groups and nonpositively curved groups 20F55 Reflection and Coxeter groups (group-theoretic aspects)
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