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MiS Preprint
101/2002
Regular Connections among Generalized Connections
Christian Fleischhack
Abstract
The properties of the space $\cal A$ of regular connections as a subset of the space $\overline{\cal A}$ of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths it is determined whether $\cal A$ is dense in $\overline{\cal A}$ or not. Moreover, it is proven that $\cal A$ has Ashtekar-Lewandowski measure zero for every nontrivial structure group and every smoothness category. The analogous results hold for gauge orbits instead of connections.
