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 $\mathbb{R}$.

47 pages, comments welcome. v3: The operad has been renamed. The abstract, introduction and background sections have been rewritten with a more expert audience in mind and pared down. The terrestrially bound graph complexes have been introduced in Section 5.1

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Cited by in corpus (2)

• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• Configuration-mapping spaces and homology stability