Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic groups under mild orientability conditions on the JSJ decomposition.
Embeddings and the (virtual) cohomological dimension of the braid and mapping class groups of surfaces
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Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic groups under mild orientability conditions on the JSJ decomposition.