The mapping class group of a handlebody is a virtual duality group, with the dualising module of torsion-free finite-index subgroups described as the homology of the complex of non-simple disc systems in positive genus.
Homotopy type of the complex of free factors of a free group
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The handlebody group is a virtual duality group
The mapping class group of a handlebody is a virtual duality group, with the dualising module of torsion-free finite-index subgroups described as the homology of the complex of non-simple disc systems in positive genus.