Hierarchically hyperbolic groups, products of $\textrm{CAT(-1)}$ spaces, and virtual torsion-freeness

Abstract

We prove that a group acting geometrically on a product of proper minimal $\textrm{CAT}(-1)$ spaces without permuting isometric factors is a hierarchically hyperbolic group. As an application we construct hierarchically hyperbolic groups which are not virtually torsion-free.

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