Homotopy type of Euclidean configuration spaces (Q2722349)

Let \(F({\mathbb R}^n, k)\) denote the configuration space of pairwise-disjoint \(k\)-tuples of points in \({\mathbb R}^n\). In this short note the author describes a cellular structure for \(F({\mathbb R}^n, k)\) when \(n \geq 3\). From results in [\textit{F. R. Cohen, T. J. Lada} and \textit{J. P. May}, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of \(F({\mathbb R}^n, k)\) is well-understood. This allows an identification of the location of the cells of \(F({\mathbb R}^n, k)\) in a minimal cell decomposition. Somewhat more detail is provided by the main result here, in which the attaching maps are identified as higher order Whitehead products.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00020].