  The machinery of noncommutative geometry is applied to a space of
connections. A noncommutative function algebra of loops closely related to
holonomy loops is investigated. The space of connections is identified as a
projective limit of Lie-groups composed of copies of the gauge group. A
spectral triple over the space of connections is obtained by factoring out the
diffeomorphism group. The triple consist of equivalence classes of loops acting
on a separable hilbert space of sections in an infinite dimensional Clifford
bundle. We find that the Dirac operator acting on this hilbert space does not
fully comply with the axioms of a spectral triple.
