Equivariant formality and the cohomology of subgroups of right-angled Coxeter groups

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Vladimir Gorchakov, University of Western Ontario

Online Talk 

Real moment-angle complexes admit natural actions of elementary abelian 2-groups. In this talk, we will discuss which subgroups act equivariantly formally. For flag complexes, we give a combinatorial characterization in terms of the underlying graph. In this case, we will see how homotopy quotients(i.e. Borel constructions) of real moment-angle complexes provide classifying spaces for all coabelian subgroups of right-angled Coxeter groups, generalizing the well-known models for a right-angled Coxeter group and its commutator subgroup. This identifies their group cohomology with Borel equivariant cohomology and gives a criterion for its freeness as a module over a polynomial ring. This is joint work with Steven Amelotte.