Formality of a higher-codimensional Swiss-Cheese operad

Author

N. I.

Publication

In: Algebr. Geom. Topol. 22.1 (2022), pp. 55–111.

Online on

Online on September 20, 2018.

Accepted on

Accepted on December 8, 2020.

Updated on

Updated on November 3, 2020.

Full text

Full text.

10.2140/agt.2022.22.55

10.2140/agt.2022.22.55.

arXiv:1809.07667

arXiv:1809.07667.

hal-01878406

hal-01878406.

MR4413816

MR4413816.

Zbl07518301

Zbl07518301.

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 ℝ.