On asymptotically hereditarily aspherical groups

Abstract

We undertake a systematic study of asymptotically hereditarily aspherical (AHA) groups - the class of groups introduced by Tadeusz Januszkiewicz and the second author as a tool for exhibiting exotic properties of systolic groups. We provide many new examples of AHA groups, also in high dimensions. We relate 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 boundary at infinity for few classes of AHA groups.

36 pages, minor modifications to v1

References in corpus (2)

• A combinatorial non-positive curvature I: weak systolicity
• Boundaries of systolic groups

Cited by in corpus (7)

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