nLab
Fadell's configuration space

Given a manifold $M$, the Fadell’s configuration space (in topology called simply configuration space) is the manifold of $N$-tuples of pairwise distinct points in $M$.

It is important in the study of topological fibrations, in the study of arrangements of hyperplanes, of Knizhnik-Zamolodchikov connections and in study of geometry of renormalization.

• Edward Fadell, Lee Neuwirth, Configuration spaces Math. Scand. 10 (1962) 111-118, MR141126, pdf
• Craig Westerland, Configuration spaces in geometry and topology, 2011, pdf
• Graeme Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213–221. MR 0331377
• Edward R. Fadell, Sufian Y. Husseini, Geometry and topology of configuration spaces, Springer Monographs in Mathematics (2001), MR2002k:55038, xvi+313 pp.
• F. R. Cohen, S. Gitler, On loop spaces of configuration spaces, Trans. Amer. Math. Soc. 354 (2002), no. 5, 1705–1748, MR2002m:55020