Equivariant Cohomology for Cyclic Groups

Article Type

Research Article

Publication Title

International Mathematics Research Notices

Abstract

In this paper, we compute the RO(Cn)-graded coefficient ring of equivariant cohomology for cyclic groups Cn, in the case of Burnside ring coefficients, and in the case of constant coefficients. We use the invertible Mackey functors under the box product to reduce the gradings in the computation from RO(Cn) to those expressable as combinations of λd for divisors d of n, where λ is the inclusion of Cn in S1 as the roots of unity. We make explicit computations for the geometric fixed points for Burnside ring coefficients and in the positive cone for constant coefficients. The positive cone is also computed for the Burnside ring in the case of prime power order and square free order. Finally, we also make computations at negative gradings for the constant coefficients.

DOI

10.1093/imrn/rnaf150

Publication Date

6-1-2025

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