Geometry/topology Seminar
Tuesday, January 13, 2009, 4:30pm, 119 Physics
Andrew Putman (MIT)
The second rational homology group of the moduli space of curves with level structures

Abstract:

Let G be a finite-index subgroup of the mapping class group of a closed genus g surface that contains the Torelli group. For instance, G can be the level L subgroup or the spin mapping class group. We show that H_2(G;Q) = Q for g > 4. A corollary of this is that the rational Picard groups of the associated finite covers of the moduli space of curves are equal to Q.

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