This entry is superceded by configuration space of points. See there for more.
Given a manifold , the Fadell’s configuration space (in topology called simply configuration space) is the manifold of -tuples of pairwise distinct points in .
It is important in the study of topological fibrations, in the study of arrangements of hyperplanes, of Knizhnik-Zamolodchikov connection and in study of geometry of renormalization.
See at configuration space of points for more.
Let . Then
the unordered configuration space of points in is a model for the classifying space of the symmetric group ;
the ordered configuration space of points, equipped with the canonical -action, is a model for the -universal principal bundle.
Edward Fadell, Lee Neuwirth, Configuration spaces
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 (pdf)
Edward Fadell, Sufian Husseini, Geometry and topology of configuration spaces, Springer Monographs in Mathematics (2001), MR2002k:55038, xvi+313 pp.
Fred Cohen, S. Gitler, On loop spaces of configuration spaces, Trans. Amer. Math. Soc. 354 (2002), no. 5, 1705–1748, MR2002m:55020
Last revised on October 9, 2019 at 18:27:45. See the history of this page for a list of all contributions to it.