# The stable moduli space of Riemann surfaces: Mumford's conjecture

@article{Madsen2002TheSM, title={The stable moduli space of Riemann surfaces: Mumford's conjecture}, author={Ib Henning Madsen and Michael Weiss}, journal={Annals of Mathematics}, year={2002}, volume={165}, pages={843-941} }

D.Mumford conjectured in (30) that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes i of di- mension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by B 1, where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of "large" genus. Tillmann's insight (41) that the plus construction makes B 1 into an infinite loop…

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