Mod p homology of the stable mapping class group

Abstract

We calculate the homology $\text{H}{}_{\mathrm{\ast }}\text{(Γ}{}_{\mathrm{g,n}}\text{;}\text{F}{}_{\mathrm{p}}\text{)}$ of the mapping class group Γ_g,n in the stable range. The calculation is based on Madsen and Weiss’ proof of the “Generalised Mumford Conjecture”: Γ_g,n has the same homology as a component of the space $\text{Ω}{}^{\mathrm{\infty }}\text{C}\text{P}{}_{\mathrm{-1}}{}^{\mathrm{\infty }}$ in the stable range.