# nLab universal connection

### Context

#### $\infty$-Chern-Weil theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

## Theorems

#### Differential cohomology

differential cohomology

# Contents

## Idea

For $G$ a compact Lie group there is a way to equip the topological classifying space $B G$ with smooth structure such that the corresponding smooth universal principal bundle $E G \to B G$ carries a smooth connection $\nabla_{univ}$ with the property that for every $G$-principal bundle $P \to X$ with connection $\nabla$ there is a smooth representative $f : X \to B G$ of the classifying map, such that $(P, \nabla) \simeq (P, f^* \nabla_{univ})$. This $\nabla_{univ}$ is called the universal $G$-connection.

## References

• M. S. Narasimhan and S. Ramanan,

Existence of universal connections , Amer. J. Math. 83 (1961), 563–572. MR 24 #A3597

Existence of universal connections II , Amer. J. Math. 85 (1963), 223–231. MR 27 #1904

Created on May 8, 2011 21:45:12 by Urs Schreiber (217.41.226.95)