Mod \(p\) homology of the stable mapping class group (Q1879802)

Let \(F_{g,n}\) be an oriented surface of genus \(g\) with \(n\) boundary components and let \(\Gamma_{g,n}\) denote the mapping class group of \(F_{g,n}\), the group of isotopy classes of orientation-preserving diffeomorphisms of \(F_{g,n}\) fixing each point in a neighborhood of the boundary of \(F_{g,n}\). In this paper the author calculates the homology groups \(H_*(F_{g,n};{\mathbb{F}}_p)\) in the stable range. The calculation is based on the proof of Mumford Conjecture given by I. Madsen and M. Weiss.