Formality of a higher-codimensional Swiss-Cheese operad

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Preprint v1, 40 pages
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PDF arXiv:1809.07667 hal-01878406

We study configurations of points in the complement of a linear subspace inside a Euclidean space, $\mathbb{R}^{n} \setminus \mathbb{R}^{m}$ with $n - m \ge 2$. We define a higher-codimensional Swiss-Cheese operad $\mathsf{VSC}_{mn}$ associated to such configurations, a variant of the classical Swiss-Cheese operad. The operad $\mathsf{VSC}_{mn}$ 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 $\mathbb{R}$.