nLab
Fadell's configuration space

This entry is superceded by configuration space of points. See there for more.

Contents

Idea

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

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.

Examples

Classifying space of the symmetric group

Let X= X= \mathbb{R}^\infty. Then

References