Twisted homology of symmetric groups

Abstract

We study the homology of symmetric groups $\Sigma _{n}$ with coefficients coming from the functor $T:\textit {finite\ pointed\ sets }\to Ab$. We are primarily interested in the limit $co\lim _{n}H_{*}(\Sigma _{n};T([n]))$ where $[n]=\{ 0,1,...,n\}$. Our main goal is to compare the described above situation with the case of general linear groups.