MiS Preprint Repository

The action of Ashtekar's generalized gauge group $\bar{\mathrm{G}}$ on the space $\bar{\mathrm{A}}$ of generalized connections is investigated for compact structure groups $G$. First a stratum is defined to be the set of all connections of one and the same gauge orbit type, i.e. the conjugacy class of the centralizer of the holonomy group. Then a slice theorem is proven on $\bar{\mathrm{A}}$. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, $\bar{\mathrm{A}}$ is topologically regularly stratified by $\bar{\mathrm{G}}$. These results coincide with those of Kondracki and Rogulski for Sobolev connections. As a by-product, we prove that the set of all gauge orbit types equals the set of all (conjugacy classes of) Howe subgroups of $G$. Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.