Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of ${\rm{Out}}(F_N)$
Group Theory
2025-03-26 v2 Algebraic Topology
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 in terms of the local cohomology cosheaf of the spine of Outer space.
Cite
@article{arxiv.2405.05881,
title = {Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of ${\rm{Out}}(F_N)$},
author = {Richard D. Wade and Thomas A. Wasserman},
journal= {arXiv preprint arXiv:2405.05881},
year = {2025}
}
Comments
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