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.
1
Brandeis University, Waltham, USA
2
Lehman College and The Graduate Center, City University of New York, USA
Carolyn Abbott; Jason Behrstock. Conjugator lengths in hierarchically hyperbolic groups. Groups, geometry, and dynamics, Tome 17 (2023) no. 3, pp. 805-838. doi: 10.4171/ggd/722
@article{10_4171_ggd_722,
author = {Carolyn Abbott and Jason Behrstock},
title = {Conjugator lengths in hierarchically hyperbolic groups},
journal = {Groups, geometry, and dynamics},
pages = {805--838},
year = {2023},
volume = {17},
number = {3},
doi = {10.4171/ggd/722},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/722/}
}
TY - JOUR
AU - Carolyn Abbott
AU - Jason Behrstock
TI - Conjugator lengths in hierarchically hyperbolic groups
JO - Groups, geometry, and dynamics
PY - 2023
SP - 805
EP - 838
VL - 17
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/722/
DO - 10.4171/ggd/722
ID - 10_4171_ggd_722
ER -
%0 Journal Article
%A Carolyn Abbott
%A Jason Behrstock
%T Conjugator lengths in hierarchically hyperbolic groups
%J Groups, geometry, and dynamics
%D 2023
%P 805-838
%V 17
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/722/
%R 10.4171/ggd/722
%F 10_4171_ggd_722
