Formality of a higher-codimensional Swiss-Cheese operad

Najib Idrissi (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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 $\mathbb{R}$.

Domaines: Topologie algébrique [math.AT]

Najib Idrissi. Formality of a higher-codimensional Swiss-Cheese operad. 2019. ⟨hal-01878406v2⟩