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- Title
Conjugator lengths in hierarchically hyperbolic groups.
- Authors
Abbott, Carolyn; Behrstock, Jason
- Abstract
In this paper, we establish upper bounds on the length of the shortest conjugator between pairs of infinite order elements in a wide class of groups. We obtain a general result which applies to all hierarchically hyperbolic groups, a class which includes mapping class groups, right-angled Artin groups, Burger-Mozes-type groups, most 3-manifold groups, and many others. In this setting, we establish a linear bound on the length of the shortest conjugator for any pair of conjugate Morse elements. For a subclass of these groups, including, in particular, all virtually compact special groups, we prove a sharper result by obtaining a linear bound on the length of the shortest conjugator between a suitable power of any pair of conjugate infinite order elements.
- Subjects
HYPERBOLIC groups; COMPACT groups; ARTIN algebras; HYPERBOLIC spaces
- Publication
Groups, Geometry & Dynamics, 2023, Vol 17, Issue 3, p805
- ISSN
1661-7207
- Publication type
Article
- DOI
10.4171/GGD/722