group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
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).
The conjecture is due to
The proof is due to
See also
Geoffrey Powell, The Mumford conjecture (after Madsen and Weiss), Séminaire Bourbaki. Vol. 2004/2005. Astérisque 307 (2006), Exp. No. 944, viii, 247–282, MR2009f:55018
Michael Weiss, Cohomology of the stable mapping class group, Topology, geometry and quantum field theory, 379–404, London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press 2004, MR2005e:57059
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
Review and exposition is in
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