A Direct Computation of the Cohomology of the Braces Operad

TL;DR

This paper provides a purely combinatorial proof that the cohomology of the braces operad is the Gerstenhaber operad, clarifying its algebraic structure.

Contribution

It offers a new, self-contained combinatorial proof of the cohomology of the braces operad being the Gerstenhaber operad, enhancing understanding of their relationship.

Findings

Confirmed the cohomology of the braces operad is the Gerstenhaber operad

Provided a self-contained combinatorial proof

Clarified the algebraic structure of the braces operad

Abstract

We give a self-contained and purely combinatorial proof of the well known fact that the cohomology of the braces operad is the operad $\mathsf{Ger}$ governing Gerstenhaber algebras.