Weight 11 compactly supported cohomology of moduli spaces of curves

TL;DR

This paper investigates the weight 11 component of the compactly supported cohomology of moduli spaces of curves, revealing new nonvanishing results and growth patterns as genus increases, using graph complex methods.

Contribution

It introduces novel techniques to analyze specific cohomology weights of moduli spaces and establishes new nonvanishing and growth results for these cohomologies.

Findings

Proves nonvanishing of certain cohomology groups for moduli spaces of curves.

Shows exponential growth of cohomology dimensions with genus.

Utilizes graph complex techniques to analyze cohomology structures.

Abstract

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