Weight 11 Compactly Supported Cohomology of Moduli Spaces of Curves in excess four

TL;DR

This paper extends the computation of the weight 11 compactly supported cohomology of moduli spaces of curves to excess four graph complexes, providing detailed methods and explicit results.

Contribution

It introduces the computation of cohomology for excess four graph complexes, expanding previous work on lower excess cases with detailed methodology.

Findings

Computed cohomology for excess four graph complexes

Provided explicit descriptions of generators and computation process

Extended the understanding of moduli space cohomology in higher excess cases

Abstract

In their homonymous article, Sam Payne and Thomas Willwacher construct a combinatorial graph complex to compute the weight 11 part of the compactly supported cohomology of the moduli space of curves $\cM_{g,n}$ and compute explicitly the cohomology of the introduced graph complexes in cases of complexes of excess zero, one, two, and three. In this paper, we extend the computation the cohomology to excess four graph complexes. Along the way, we give more details on generators, the computation process, and the definition of the graph complex.