Summary: All algebraic objects in this note will be considered over a fixed field $k$ of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over $k$. For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95,...

Let $F({ℝ}^n,k)$ denote the configuration space of pairwise-disjoint $k$-tuples of points in ${ℝ}^n$. In this short note the author describes a cellular structure for $F({ℝ}^n,k)$ when $n\ge 3$. From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of $F({ℝ}^n,k)$ is well-understood. This allows an identification of the location of the cells of $F({ℝ}^n,k)$ in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...