Real models for the framed little $n$-disks operads

Abstract

We study the action of the orthogonal group on the little $n$-disks operads. As an application we provide small models (over the reals) for the framed little $n$-disks operads. It follows in particular that the framed little $n$-disks operads are formal (over the reals) for $n$ even and coformal for all $n$.

The 2025 version of this paper is a thoroughly revised and extended version of the original 2017 version, repairing several mistakes and shortcomings. The paper is to appear in the Journal of Topology

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Cited by in corpus (6)

• (Non-)formality of the extended Swiss Cheese operads
• A model for framed configuration spaces of points
• Moduli problems for operadic algebras
• On the homotopy type of the spaces of spherical knots in $R^n$
• Formality of a higher-codimensional Swiss-Cheese operad
• Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules