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

Abstract

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 $\mathrm{Out}(F_N)$ in terms of the local cohomology cosheaf of the spine of Outer space.

arXiv commentAccepted version at IMRN. Theorem E in this version is new, and gives an abstract way to bound the rank of the rational cohomology of Out(F_n) in the vcd

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