(Non-)formality of the extended Swiss Cheese operads

Abstract

We study two colored operads of configurations of little $n$-disks in a unit $n$-disk, with the centers of the small disks of one color restricted to an $m$-plane, $m<n$. We compute the rational homotopy type of these \emph{extended Swiss Cheese operads} and show how they are connected to the rational homotopy types of the inclusion maps from the little $m$-disks to the little $n$-disks operad.

For v2 a mistake in the appendix was repaired, the appendix revised and integrated as a section into the main part of the paper

References in corpus (2)

• Coloured Koszul duality and strongly homotopy operads
• Real models for the framed little $n$-disks operads

Cited by in corpus (7)

• Configuration Spaces of Manifolds with Boundary
• Configuration-mapping spaces and homology stability
• Formality of a higher-codimensional Swiss-Cheese operad
• Vertical configuration spaces and their homology
• Non-formality of Voronov's Swiss-Cheese operads
• Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules
• Configuration spaces of clusters as $E_d$-algebras