The stable moduli space of Riemann surfaces: Mumford’s conjecture

D. Mumford conjectured in For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by B , where is the group of isotopy classes of automorphisms of a smooth oriented connected surface of "large" genus. Tillmann's theorem 44 that the plus construction makes B into an infinite loop space led to a stable homotopy version of Mumford's conjecture, stronger than the original We prove the stronger version, relying on Harer's stability theorem 17, Vassiliev's theorem concerning spaces of functions with moderate singularities