Formality of a higher-codimensional Swiss-Cheese operad

Najib Idrissi
In: Algebr. Geom. Topol. 22.1 (2022), pp. 55–111
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We study bicolored configurations of points in the Euclidean nn-space that are constrained to remain either inside or outside a fixed Euclidean mm-subspace, with nm2n - m \ge 2. We define a higher-codimensional variant of the Swiss-Cheese operad, called the complementarily constrained disks operad CDmn\mathsf{CD}_{mn}, associated to such configurations. The operad CDmn\mathsf{CD}_{mn} is weakly equivalent to the operad of locally constant factorization algebras on the stratified space {RmRn}\{\mathbb{R}^{m} \subset \mathbb{R}^{n}\}. We prove that this operad is formal over ℝ.