Lattices in a product of trees, hierarchically hyperbolic groups, and virtual torsion-freeness

TL;DR

This paper constructs examples of hierarchically hyperbolic groups that are not virtually torsion-free by creating cocompact lattices in a product of trees, challenging previous assumptions about these groups.

Contribution

It provides the first known examples of hierarchically hyperbolic groups that are not virtually torsion-free, using cocompact lattices in a product of trees.

Findings

Constructed cocompact lattices in a product of trees that are not virtually torsion-free.

First examples of hierarchically hyperbolic groups with non-virtually torsion-free property.

Abstract

We construct cocompact lattices in a product of trees which are not virtually torsion-free. This gives the first examples of hierarchically hyperbolic groups which are not virtually torsion-free