Formality of a higher-codimensional Swiss-Cheese operad

Author(s)
Najib Idrissi
Publication
In: Algebr. Geom. Topol. 22.1 (2022), pp. 55–111
Online on
Updated on
Accepted on

Abstract

We study bicolored configurations of points in the Euclidean $n$-space that are constrained to remain either inside or outside a fixed Euclidean $m$-subspace, with $n - m \ge 2$. We define a higher-codimensional variant of the Swiss-Cheese operad, called the complementarily constrained disks operad $\mathsf{CD}_{mn}$, associated to such configurations. The operad $\mathsf{CD}_{mn}$ is weakly equivalent to the operad of locally constant factorization algebras on the stratified space $\{\mathbb{R}^{m} \subset \mathbb{R}^{n}\}$. We prove that this operad is formal over ℝ.