The volume of the moduli space of flat connections on a nonorientable 2-manifold

摘要

We compute the Riemannian volume of the moduli space of flat connections on a nonorientable 2-manifold, for a natural class of metrics. We also show that Witten's volume formula for these moduli spaces may be derived using Haar measure, and we give a new proof of Witten's volume formula for the moduli space of flat connections on a 2-manifold using Haar measure.