$E_{\infty }$-cells and general linear groups of finite fields

Abstract

We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_{\infty }$-algebras, guided by computations of homology with coefficients in the $E_1$-split Steinberg module.

32 pages, final version to appear in Annales scientifiques de l'École normale supérieure