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- Title
Unbounded domains in hierarchically hyperbolic groups.
- Authors
Petyt, Harry; Spriano, Davide
- Abstract
We investigate unbounded domains in hierarchically hyperbolic groups and obtain constraints on the possible hierarchical structures. Using these insights, we characterise the structures of virtually abelian HHGs and show that the class of HHGs is not closed under finite extensions. This provides a strong negative answer to the question of whether being an HHG is invariant under quasi-isometries. Along the way, we show that infinite torsion groups are not HHGs. By ruling out pathological behaviours, we are able to give simpler, direct proofs of the rank-rigidity and omnibus subgroup theorems for HHGs. This involves extending our techniques so that they apply to all subgroups of HHGs.
- Subjects
INFINITE groups; HYPERBOLIC groups
- Publication
Groups, Geometry & Dynamics, 2023, Vol 17, Issue 2, p479
- ISSN
1661-7207
- Publication type
Article
- DOI
10.4171/GGD/706