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