Contents

# Contents

## Idea

Given a space $X$ and a group $G$, a $G$-flat connection or $G$-local system is a map $X \to \flat \mathbf{B}G$, or equivalently a map $\Pi(X) \to \mathbf{B}G$. A moduli space of flat connections is a moduli space/moduli stack of such structure.

## Examples

The moduli space of flat connections for suitable Lie groups over Riemann surfaces appears as the phase space of $G$-Chern-Simons theory over these surfaces. It carries itself a projectively flat connection, the Knizhnik-Zamolodchikov connection or Hitchin connection.

## Properties

The Narasimhan–Seshadri theorem asserts that the moduli space of flat connections on a Riemann surface is naturally a complex manifold.

## References

• Jörg Teschner, Quantization of moduli spaces of flat connections and Liouville theory, proceedings of the International Congress of Mathematics 2014 (arXiv:1405.0359)

For more see the references at moduli space of connections.

Last revised on October 14, 2019 at 12:51:33. See the history of this page for a list of all contributions to it.