Contents

cohomology

complex geometry

# Contents

## Idea

A conjecture in (Mumford 83) concerned the ordinary cohomology with rational numbers coefficients of the classifying space of the stable mapping class group, which is essentially the stable orbifold cohomology of the moduli stack of curves over the complex numbers.

The conjecture was proven in (Madsen-Weiss 02).

Exposition and review is in (Madsen 07).

## References

The conjecture is due to

• David Mumford, Towards an enumerative geometry of the moduli space of curves, In Arithmetic and geometry, Vol. II, Progr. Math. 36, Birkhäuser, Boston, MA, 1983, 271–328.

The proof is due to

• Ib Madsen, Ulrike Tillmann, The stable mapping class group and $Q(\mathbf{C} P^\infty_+)$, Invent. Math. 145 (2001), no. 3, 509–544. MR2002h:55011