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arXiv · 2009.08526

The equivariant cohomology for semidirect product actions

Sergio Chaves
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Abstract

The rational Borel equivariant cohomology for actions of a compact connected Lie group is determined by restriction of the action to a maximal torus. We show that a similar reduction holds for any compact Lie group $G$ when there is a closed subgroup $K$ such that the cohomology of the classifying space $BK$ is free over the cohomology of $BG$ for field coefficients. We study the particular case when $G$ is a semi-direct product and $K$ is its maximal elementary abelian 2-subgroup for cohomology with coefficients in a field of characteristic two. This provides a different approach to investigate the syzygy order of the equivariant cohomology of a space with a torus action and a compatible involution, and we relate this description with results for 2-torus actions.

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Sergio Chaves. 2024-02-13. The equivariant cohomology for semidirect product actions. https://arxiv.org/abs/2009.08526

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