nLab moduli space of flat connections




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


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


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

moduli spaces


For more see the references at moduli space of connections.

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

Introducing Fock-Goncharov coordinates on moduli spaces of flat connections:

Last revised on April 14, 2024 at 05:16:08. See the history of this page for a list of all contributions to it.