Equivariant formality and the cohomology of subgroups of right-angled Coxeter groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911616219480064 |
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| author | Amelotte, Steven Gorchakov, Vladimir |
| author_facet | Amelotte, Steven Gorchakov, Vladimir |
| contents | We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-known models for the classifying space of a right-angled Coxeter group and its commutator subgroup. This identifies the cohomology of these groups with the Borel equivariant cohomology of elementary abelian $2$-group actions on cubical subcomplexes of a cube $[-1,1]^m$. We then characterize equivariant formality for these actions, leading to a simple graph-theoretic criterion for when the cohomology of a coabelian subgroup is free as a module over the cohomology of the quotient by the commutator subgroup of the right-angled Coxeter group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20808 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant formality and the cohomology of subgroups of right-angled Coxeter groups Amelotte, Steven Gorchakov, Vladimir Algebraic Topology Group Theory 20F55, 20J06, 55N91, 55R35, 57S12, 57S17, 57M07 We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-known models for the classifying space of a right-angled Coxeter group and its commutator subgroup. This identifies the cohomology of these groups with the Borel equivariant cohomology of elementary abelian $2$-group actions on cubical subcomplexes of a cube $[-1,1]^m$. We then characterize equivariant formality for these actions, leading to a simple graph-theoretic criterion for when the cohomology of a coabelian subgroup is free as a module over the cohomology of the quotient by the commutator subgroup of the right-angled Coxeter group. |
| title | Equivariant formality and the cohomology of subgroups of right-angled Coxeter groups |
| topic | Algebraic Topology Group Theory 20F55, 20J06, 55N91, 55R35, 57S12, 57S17, 57M07 |
| url | https://arxiv.org/abs/2604.20808 |