Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of ${\rm{Out}}(F_N)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916661195440128 |
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| author | Wade, Richard D. Wasserman, Thomas A. |
| author_facet | Wade, Richard D. Wasserman, Thomas A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of ${\rm{Out}}(F_N)$ Wade, Richard D. Wasserman, Thomas A. Group Theory Algebraic Topology 55M05, 20J06 (Primary) 20F34, 20F65 (Secondary) 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. |
| title | Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of ${\rm{Out}}(F_N)$ |
| topic | Group Theory Algebraic Topology 55M05, 20J06 (Primary) 20F34, 20F65 (Secondary) |
| url | https://arxiv.org/abs/2405.05881 |