An orbifold partition of ${\overline{M}}_g^n$

Abstract

We define a partition of ${\overline{M}}_g^n$ and show that the cohomology of ${\overline{M}}_g^n$ in a given degree admits a filtration whose respective quotients are isomorphic to the shifted cohomology groups of the parts if $g$ is sufficiently large. This implies that the map $H^k({\overline{M}_g^n}) \ra H^k(M_g^n)$ is onto and that the Hodge structure of $H^k(M_g^n)$ is pure of weight $k$ if $g\ge 2k+1$. Our main ingredient is the stability theorem of Harer and Ivanov.

16 pages, Latex Version 2.09, will appear in The Moduli space of Curves (eds. Dijkgraaf, Faber, van der Geer), Progress in Math., Birkh"auser

References in corpus (1)

• Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map