The Quotient Criterion for Syzygies in Equivariant Cohomology for Elementary Abelian 2-Group Actions

Let G be a elementary abelian 2-group and X be a manifold with a locally standard action of G. We provide a criterion to determine the syzygy order of the G-equivariant cohomology of X with coefficients over a field of characteristic two using a complex associated to the cohomology of the face filtration of the manifold with corners X/G. This result is the real version of the quotient criterion for locally standard torus actions.