Weight 11 Compactly Supported Cohomology of Moduli Spaces of Curves.

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. [ABSTRACT FROM AUTHOR]