Conjugator lengths in hierarchically hyperbolic groups

  • Carolyn Abbott

    Brandeis University, Waltham, USA
  • Jason Behrstock

    Lehman College and The Graduate Center, City University of New York, USA
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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.

Cite this article

Carolyn Abbott, Jason Behrstock, Conjugator lengths in hierarchically hyperbolic groups. Groups Geom. Dyn. 17 (2023), no. 3, pp. 805–838

DOI 10.4171/GGD/722