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Journal Articles Algebraic and Geometric Topology Year : 2022

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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Dates and versions

hal-01878406 , version 1 (21-09-2018)
hal-01878406 , version 2 (17-07-2019)
hal-01878406 , version 3 (03-11-2020)

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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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