The Bredon equivariant cohomology of a point for cyclic groups

TL;DR

This paper investigates the algebraic structure of Bredon cohomology for cyclic groups of odd order, connecting it to stable homotopy groups of spheres within the derived category framework.

Contribution

It provides a detailed algebraic analysis of the RO(G)-graded Bredon cohomology for cyclic groups of odd order, extending previous research and focusing on the derived category approach.

Findings

Algebraic description of Bredon cohomology for cyclic groups of odd order

Connection established between cohomology and stable homotopy groups of spheres

Methodology based on modules over the Mackey ring

Abstract

We study the $RO(G)$-graded Bredon cohomology of a point in the case where $G$ is a cyclic group of odd order, expanding on the information provided by previous studies. Our methods center on the purely algebraic aspects of this matter, which interpret it as the "stable homotopy groups of spheres" problem for the derived category of modules over the constant-coefficient Mackey ring.