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

Richard D. Wade; Thomas A. Wasserman

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

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arxiv 2405.05881 v2 pith:7XN4U2W3 submitted 2024-05-09 math.GR math.AT

Richard D. Wade , Thomas A. Wasserman This is my paper · ORCID

classification math.GRmath.AT

keywords dualitycohen--macaulaybieri--eckmanncomplexesdualizinggroupsmoduleclassifying

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

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