Structure of $C_{pq}$-cohomology of points and slice tower

TL;DR

This paper computes the ring structure of $C_{pq}$-cohomology in positive degrees and determines the slices of certain spectra, advancing understanding of equivariant cohomology for cyclic groups.

Contribution

It extends previous additive cohomology computations to include ring structures and slice calculations for spectra involving $C_{pq}$ groups.

Findings

Ring structure in positive degrees of $C_{pq}$-cohomology computed.

Slices of the spectrum $S^V \uwedge H$ determined for any representation V.

Enhanced understanding of the structure of equivariant cohomology theories.

Abstract

The additive structure of the $RO(C_{pq})$-graded Bredon cohomology $S^0$ with coefficients in the constant Mackey functor was computed in \cite{BG19}. Using that computation, the ring structure in the positive degrees has been computed here. Further, we calculate the slices of the spectrum $S^V \wedge H\uZ$ for any representation $V.$