nLab
Fadell's configuration space

Contents

This entry is superceded by configuration space of points.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

  • the unordered configuration space of nn points in \mathbb{R}^\infty is a model for the classifying space BΣ(n)B \Sigma(n) of the symmetric group Σ(n)\Sigma(n);

  • the ordered configuration space of nn points, equipped with the canonical Σ(n)\Sigma(n)-action, is a model for the Σ(n)\Sigma(n)-universal principal bundle.

References

Last revised on October 9, 2019 at 14:27:45. See the history of this page for a list of all contributions to it.