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Homotopy type of Euclidean configuration spaces

Salvatore, Paolo — 2001

Proceedings of the 20th Winter School "Geometry and Physics"

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

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