TL;DR
This paper computes high-loop order graph cohomology, specifically at 11 loops, and uses these results to challenge a conjecture by F. Brown with a counterexample.
Contribution
It provides the first detailed computation of 11-loop graph cohomology and addresses a conjecture in the field, offering a counterexample to a strong version.
Findings
Computed the Kontsevich graph cohomology at 11 loops.
Provided counterexample to a conjecture of F. Brown.
Extended understanding of graph cohomology in higher loops.
Abstract
We compute the Kontsevich graph cohomology in loop order 11, and for some degrees in higher loop order. We apply our results to discuss a conjecture of F. Brown, providing a counterexample to a strong version of the conjecture.
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