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 -space that are constrained to remain either inside or outside a fixed Euclidean -subspace, with . We define a higher-codimensional variant of the Swiss-Cheese operad, called the complementarily constrained disks operad , associated to such configurations. The operad is weakly equivalent to the operad of locally constant factorization algebras on the stratified space . We prove that this operad is formal over ℝ.