Minimal models, GT-action and formality of the little disk operad

TL;DR

This paper provides a new proof of the formality of the little disks operad using operadic formality criteria and the action of the Grothendieck-Teichmüller group, linking algebraic and topological structures.

Contribution

It introduces a novel proof of the little disks operad's formality leveraging operadic Sullivan criteria and Grothendieck-Teichmüller group actions.

Findings

Proof of formality via operadic Sullivan criterion

Connection between Grothendieck-Teichmüller group and operad formality

Operadic methods simplify understanding of little disks operad

Abstract

We give a new proof of formality of the operad of little disks. The proof makes use of an operadic version of a simple formality criterion for commutative differential graded algebras due to Sullivan. We see that formality is a direct consequence of the fact that the Grothendieck-Teichm\"uller group operates on the chain operad of little disks.