MiS Preprint Repository

The bundle structure of the space $\bar{A}$ of Ashtekar\'s generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space $\bar{G}$ of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space $\bar{A}$. However, for a certain class of non-abelian gauge theories - e.g., all SU(N) theories - the generic stratum is nontrivial. This means, there are no global gauge fixings - the so-called Gribov problem. Nevertheless, there is a covering of the generic stratum by trivializations each having total induced Haar measure 1.