A short treatise on Equivariant Gamma spaces

TL;DR

This paper establishes a formal connection between equivariant Gamma spaces and orthogonal spectra, demonstrating their equivalence in modeling equivariant infinite loop spaces through a connective Quillen equivalence.

Contribution

It introduces a connective Quillen equivalence between the categories of equivariant Gamma spaces and orthogonal spectra, advancing the theoretical understanding of equivariant stable homotopy theory.

Findings

Establishes a Quillen equivalence between equivariant Gamma spaces and orthogonal spectra.

Shows that both models are suitable for representing equivariant infinite loop spaces.

Provides a theoretical foundation for translating results between these two frameworks.

Abstract

Equivariant $\Gamma$-spaces model equivariant infinite loop spaces. In this article, we show that there exists a connective Quillen equivalence between the category of equivariant $\Gamma$-spaces and the category of orthogonal spectra.