JP Journal of Geometry and Topology

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EQUIVARIANT COHOMOLOGY FOR SEMIDIRECT PRODUCT ACTIONS

Authors

  • Sergio Chaves

Keywords:

equivariant cohomology, syzygies, compact Lie groups, semidirect product

DOI:

https://doi.org/10.17654/0972415X24006

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 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.

Received: April 21, 2024
Revised: May 23, 2024
Accepted: June 10, 2024

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Published

2024-12-24

Issue

Vol. 30 No. 2 (2024)

Section

Articles

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How to Cite

EQUIVARIANT COHOMOLOGY FOR SEMIDIRECT PRODUCT ACTIONS. (2024). JP Journal of Geometry and Topology, 30(2), 83-104. https://doi.org/10.17654/0972415X24006

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