  Given a principal bundle on an orientable closed surface with compact
connected structure group, we endow the space of based gauge equivalence
classes of smooth connections relative to smooth based gauge transformations
with the structure of a Fr\'echet manifold. Using Wilson loop holonomies and a
certain characteristic class determined by the topology of the bundle, we then
impose suitable constraints on that Fr\'echet manifold that single out the
based gauge equivalence classes of central Yang-Mills connections but do not
directly involve the Yang-Mills equation. We also explain how our theory yields
the based and unbased gauge equivalence classes of all Yang-Mills connections
and deduce the stratified symplectic structure on the space of unbased gauge
equivalence classes of central Yang-Mills connections. The crucial new
technical tool is a slice analysis in the Fr\'echet setting.
