Equivariant cohomology for cyclic groups of square-free order

Article Type

Research Article

Publication Title

Research in Mathematical Sciences

Abstract

The main objective of this paper is to compute RO(G)-graded cohomology of G-orbits for the group G=Cn, where n is a product of distinct primes. We compute these groups for the constant Mackey functor Z̲ and the Burnside ring Mackey functor A̲. Among other results, we show that the groups H̲Gα(S0) are mostly determined by the fixed point dimensions of the virtual representations α, except in the case of A̲ coefficients when the fixed point dimensions of α have many zeros. In the case of Z̲ coefficients, the ring structure on the cohomology is also described. The calculations are then used to prove freeness results for certain G-complexes.

DOI

10.1007/s40687-024-00443-0

Publication Date

6-1-2024

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