Ranks of $RO(G)$-graded stable homotopy groups of spheres for finite groups $G$

TL;DR

This paper investigates the structure of stable homotopy groups of spheres graded by the real representation ring of finite groups, revealing how infinite groups are distributed within this framework.

Contribution

It provides a detailed description of the distribution of infinite groups in the $RO(G)$-graded stable homotopy groups for finite groups, a novel analysis in equivariant stable homotopy theory.

Findings

Characterization of infinite groups in the $RO(G)$-graded groups

Distribution patterns of these groups for various finite groups

Insights into the structure of equivariant stable homotopy groups

Abstract

We describe the distribution of infinite groups in the $RO(G)$-graded stable homotopy groups of spheres for a finite group $G$.