a Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103, Leipzig, Germany
b Center for Gravitational Physics and Geometry, 320 Osmond Lab, Penn State University, University Park, PA 16802, USA
Abstract:
The properties of the space
of regular connections as a subset of the space
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
is dense in
or not. Moreover, it is proven that
has Ashtekar–Lewandowski measure zero for every non-trivial structure group and every smoothness category. The analogous results hold for gauge orbits instead of connections.