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Formality of a higher-codimensional Swiss-Cheese operad

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 $\mathbb{R}$.
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https://hal.archives-ouvertes.fr/hal-01878406
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Submitted on : Tuesday, November 3, 2020 - 10:53:10 AM
Last modification on : Thursday, October 20, 2022 - 3:18:40 AM

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Najib Idrissi. Formality of a higher-codimensional Swiss-Cheese operad. Algebraic and Geometric Topology, 2022, 22, ⟨10.21136/HS.2021.09⟩. ⟨hal-01878406v3⟩

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