E_∞-cells and general linear groups of finite fields

2018/10/29 by Galatius, Soren, Kupers, Alexander, Randal-Williams, Oscar
#18F25 #55P48 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.11931

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_∞-algebras, guided by computations of homology with coefficients in the E₁-split Steinberg module.

Related

• E_∞-cells and general linear groups of infinite fields
• Euler class groups, and the homology of elementary and special linear groups
• Homological stability for general linear groups over Dedekind domains
• Homological stability for certain classical groups
• Unordered resolutions and homological stability for linear groups