# Formality of a higher codimensional Swiss-Cheese operad accepted in Algebraic & Geometric Topology

Published .  math  operads  paper  swiss-cheese

My paper, “Formality of a higher codimensional Swiss-Cheese operad”, has just been accepted for publication in Algebraic & Geometric Topology! This paper is part of my effort to try and apply rational homotopy theoretical methods to the computation of factorization homology and invariants of knot-like structures. As a reminder, here is its 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.

The paper went through several iterations as part of the editorial process. I am very grateful to the editorial committee for this, as well as to the anonymous referees who provided many suggestions to improve the paper, especially the exposition.

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