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arXiv · 2405.05881

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

Richard D. Wade·Thomas A. Wasserman
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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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Richard D. Wade, Thomas A. Wasserman. 2024-05-09. Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of ${\rm{Out}}(F_N)$. https://doi.org/10.1093/imrn%2Frnaf059

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