For hierarchically hyperbolic groups, the boundary is connected if and only if the group is one-ended, and free product boundaries are characterized by factor boundaries.
Hierarchically hyperbolic spaces II: Com- bination theorems and the distance formula
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On the connectedness of the boundary of hierarchically hyperbolic spaces
For hierarchically hyperbolic groups, the boundary is connected if and only if the group is one-ended, and free product boundaries are characterized by factor boundaries.