# nLab universal connection

Contents

### 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

### In bounded dimension

Universal connections for manifolds of some bounded dimension $\leq n$ are appealed to in

and discussed in detail in