Abstract
In this talk, I will explain how Witten, at the beginning of the 1990's, computed the symplectic volume of the moduli space of flat connections on a principal bundle over a closed compact surface. Witten's main idea was to approximate the Liouville measure on the space of flat connections by a measure on the space of all connections (module gauge transformations), the non-normalised Yang—Mills measure, of which the total mass is, at a heuristic level, easy to compute.
