On the $RO(G)$-graded coefficients of $Q_8$ equivariant cohomology

TL;DR

This paper computes the $RO(G)$-graded coefficients of the equivariant cohomology spectrum for the quaternion group $Q_8$, advancing understanding of equivariant stable homotopy theory for non-abelian groups.

Contribution

It provides explicit calculations of the $RO(G)$-graded coefficients of $H$, a key step in understanding $Q_8$-equivariant cohomology.

Findings

Explicit $RO(G)$-graded coefficients for $Q_8$

Enhanced understanding of $Q_8$-equivariant cohomology

Foundation for further computations in non-abelian equivariant homotopy

Abstract

In this paper, we calculate the $RO(G)$-graded coefficients of $H\underline{\mathbb{Z}}$, the Eilenberg-MacLane spectrum of constant Mackey functor for quaternion group $Q_8$.