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 with field coefficients. This provides a different approach to  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.

equivariant cohomology, syzygies, compact Lie groups, semidirect product

Received: April 21, 2024; Revised: May 23, 2024; Accepted: June 10, 2024; Published: December 24, 2024

How to cite this article: Sergio Chaves, Equivariant cohomology for semidirect product actions, JP Journal of Geometry and Topology 30(2) (2024), 83-104. https://doi.org/10.17654/0972415X24006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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