The quotient criterion for syzygies in equivariant cohomology for elementary abelian $2$-group actions

Sergio Chaves

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arXiv · 2009.08530

The quotient criterion for syzygies in equivariant cohomology for elementary abelian $2$-group actions

Sergio Chaves

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Abstract

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 developed by M. Franz in arXiv:1205.4462.

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Sergio Chaves. 2020-09-17. The quotient criterion for syzygies in equivariant cohomology for elementary abelian $2$-group actions. https://arxiv.org/abs/2009.08530

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