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.

Accepted 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

References in corpus (2)

• The boundary of bordified Outer space
• Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves

Cited by in corpus (1)

• Connectivity of partial basis complexes of freely decomposable groups