标题： 广义规范轨道空间的分层 显示英文标题

标题： Stratification of the Generalized Gauge Orbit Space

摘要： Ashtekar的广义规范群$\Gb$在广义连接空间$\Ab$上的作用对于紧致结构群$\LG$进行了研究。 首先定义一个层为具有相同规范轨道类型的全部连接的集合，即 中心化子的共轭类。 然后在$\Ab$上证明了一个截面定理。 这给出了层的开性。 之后，证明了层的稠密性定理。 因此，$\Ab$由$\Gb$拓扑正则分层。 这些结果与Kondracki和Rogulski对Sobolev连接的结果一致。 作为副产品，我们证明了所有规范轨道类型的集合等于所有$\LG$的Howe子群（共轭类）的集合。 最后，我们证明了具有最大类型的全部规范轨道的集合具有全诱导Haar测度 1. 显示英文摘要

摘要： The action of Ashtekar's generalized gauge group $\Gb$ on the space $\Ab$ of generalized connections is investigated for compact structure groups $\LG$. 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 $\Ab$. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, $\Ab$ is topologically regularly stratified by $\Gb$. 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 $\LG$. Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.