Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of $\mathrm{O}\mathrm{u}\mathrm{t}(F_N)$

We explain how Cohen–Macaulay classifying spaces are ubiquitous among discrete groups that satisfy Bieri–Eckmann duality, and compare Bieri–Eckmann duality to duality results for Cohen–Macaulay complexes. We use this comparison to give a description of the dualizing module of $\mathrm{O}\mathrm{u}\mathrm{t}(F_N)$ in terms of the local cohomology cosheaf of the spine of Outer space.