Formality of cochains on BG

TL;DR

This paper proves that the algebra of cochains on the classifying space of a compact Lie group is formal under certain invertibility conditions, simplifying its algebraic structure.

Contribution

It establishes formality of cochains on BG for compact Lie groups when the order of the Weyl group quotient is invertible in the field.

Findings

Cochains on BG are formal as an A-infinity algebra under specified conditions.

Formality holds when |N_G(T)/T| is invertible in the field k.

Simplifies the algebraic understanding of cochains on BG.

Abstract

Let $G$ be a compact Lie group with maximal torus $T$. If $|N_G(T)/T|$ is invertible in the field $k$ then the algebra of cochains $C^*(BG;k)$ is formal as an $A_\infty$ algebra, or equivalently as a DG algebra.