Contents

This entry is superceded by configuration space of points.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

# Contents

## Idea

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 connection and in study of geometry of renormalization.

See at configuration space of points for more.

## Examples

### Classifying space of the symmetric group

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

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

• the ordered configuration space of $n$ points, equipped with the canonical $\Sigma(n)$-action, is a model for the $\Sigma(n)$-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.