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- Title
Hierarchically hyperbolic groups and uniform exponential growth.
- Authors
Abbott, Carolyn R.; Ng, Thomas; Spriano, Davide; Gupta, Radhika; Petyt, Harry
- Abstract
We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hyperbolic group that is also acylindrically hyperbolic has uniform exponential growth. In addition, we provide a quasi-isometric characterization of hierarchically hyperbolic groups without uniform exponential growth. To achieve this, we gain new insights on the structure of certain classes of hierarchically hyperbolic groups. Our methods give a new unified proof of uniform exponential growth for several examples of groups with notions of non-positive curvature. In particular, we obtain the first proof of uniform exponential growth for certain groups that act geometrically on CAT(0) cubical spaces of dimension 3 or more. Under additional hypotheses, we show that a quantitative Tits alternative holds for hierarchically hyperbolic groups.
- Subjects
HYPERBOLIC groups
- Publication
Mathematische Zeitschrift, 2024, Vol 306, Issue 1, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-023-03411-6