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MiS Preprint
4/2000
Stratification of the generalized gauge orbit space
Christian Fleischhack
Abstract
The action of Ashtekar's generalized gauge group $\overline{\rm G}$ on the space $\overline{\rm A}$ 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 $\overline{\rm A}$. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, $\overline{\rm A}$ is topologically regularly stratified by $\overline{\rm G}$. 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.
