Formality of Chain Operad of Small Squares

TL;DR

This paper proves that the chain operad of small squares is formal, which simplifies understanding the proof of Kontsevich's formality theorem and relates to the existence of an associator.

Contribution

It establishes the formality of the chain operad of small squares, providing a clearer foundation for Kontsevich's formality theorem.

Findings

Chain operad of small squares is formal

Simplifies proof of Kontsevich's formality theorem

Formality follows from existence of an associator

Abstract

We prove that the chain operad of small squares is formal. This fact clarifies situation with the proof of M. Kontsevich formality theorem in the paper of the author math.QA/9803025, revised Sept 24. The formality of the operad follows quite easily from the existence of an associator.