Equivariant formality of the little disks operad

TL;DR

This paper proves that the little disks operad is equivariantly formal over the rationals, establishing its rational formality as an $ abla$-operad in both oriented and unoriented cases.

Contribution

It demonstrates the equivariant formality of the little disks operad over the rationals, extending the understanding of its algebraic and topological structure.

Findings

The little $n$-disks operad is $SO(n)$ and $O(n)$-equivariantly formal over the rationals.

The oriented and unoriented framed little disks operads are rationally formal as $ abla$-operads.

Abstract

The little $n$-disks operad is $SO(n)$ and $O(n)$-equivariantly formal over the rationals. Equivalently, the oriented and unoriented framed little disks operads are rationally formal as $\infty$-operads.