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Cohomology of diffeomorphism groups
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Riemann’s moduli space M_g classifies families of genus g Riemann surfaces, and is also a model for the classifying space of the group of diffeomorphisms of a genus g surface. In 1985 Harer proved his celebrated stability theorem, which states that the i-th cohomology of M_g is independent of g, as long as g is large compared with i. More recently, Madsen and Weiss computed the cohomology of M_g in this large genus regime, confirming a conjecture of Mumford.
I will discuss recent joint work with S. Galatius, where we establish an analogous pair of results for manifolds of higher even dimension.
This talk is part of the Special DPMMS Colloquium series.
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