Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic under orientability conditions on JSJ decompositions, via bounded central extensions of orbifold mapping class groups, with a sharpness counterexample.
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 under orientability conditions on JSJ decompositions, via bounded central extensions of orbifold mapping class groups, with a sharpness counterexample.