Given a space and a group , a -flat connection or -local system is a map , or equivalently a map . 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 -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.
For more see the references at moduli space of connections.
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.