Weight 11 Compactly Supported Cohomology of Moduli Spaces of Curves

Abstract

Abstract We study the weight 11 part of the compactly supported cohomology of the moduli space of curves ${\mathcal{M}}_{g,n}$, using graph complex techniques, with particular attention to the case $n = 0$. As applications, we prove new nonvanishing results for the cohomology of ${\mathcal{M}}_{g}$, and exponential growth with $g$, in a wide range of degrees.