#### Volume 22, issue 1 (2022)

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Formality of a higher-codimensional Swiss-cheese operad

### Najib Idrissi

Algebraic & Geometric Topology 22 (2022) 55–111
##### 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 ${CD}_{mn}$, associated to such configurations. The operad ${CD}_{mn}$ is weakly equivalent to the operad of locally constant factorization algebras on the stratified space $\left\{{ℝ}^{m}\subset {ℝ}^{n}\right\}$. We prove that this operad is formal over $ℝ$.

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##### Keywords
Fulton–MacPherson compactification, graph complexes, constrained little disks, semialgebraic forms, relative loop spaces
##### Mathematical Subject Classification 2010
Primary: 18D50, 55P48
Secondary: 55R80