Homology of infinite loop spaces

TL;DR

This paper provides an elementary formula to compute the homology groups of spectra represented by special $ extGamma$-spaces, enhancing understanding of infinite loop space homology with a novel explicit result.

Contribution

It presents an explicit formula for homology of spectra from special $ extGamma$-spaces, clarifying and making accessible a result previously known but not explicitly stated.

Findings

Derived an explicit homology formula for spectra from special $ extGamma$-spaces

Connected the homology of spectra to the structure of their representing $ extGamma$-spaces

Simplified the computation process for homology in infinite loop space theory

Abstract

For a spectrum $X$ represented by a special $\Gamma$-space $Y$ via the Segal machine, we give an elementary formula computing the homology groups of $X$ in terms of $Y$. Both the result and the method of proof are essentially due to T. Pirashvili, but the end result does not appear explicitly in his papers.