Conditions of smoothness of moduli spaces of flat connections and of representation varieties

Nan-Kuo Ho, Graeme Wilkin, Siye Wu

Published 2016-10-31Version 1

We use gauge theoretic and algebraic methods to reexamine the sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the representation variety of a finitely generated and presented group. In particular, we give a complete proof of the slice theorem for the action of the group of gauge transformations on the space of flat connections. We show that on a compact non-orientable surface, flat connections with minimal isotropy need not descend to smooth points on the moduli space.