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Given a principal bundle on an orientable closed surface with compactconnected structure group, we endow the space of based gauge equivalenceclasses of smooth connections relative to smooth based gauge transformationswith the structure of a Fr\'echet manifold. Using Wilson loop holonomies and acertain characteristic class determined by the topology of the bundle, we thenimpose suitable constraints on that Fr\'echet manifold that single out thebased gauge equivalence classes of central Yang-Mills connections but do notdirectly involve the Yang-Mills equation. We also explain how our theory yieldsthe based and unbased gauge equivalence classes of all Yang-Mills connectionsand deduce the stratified symplectic structure on the space of unbased gaugeequivalence classes of central Yang-Mills connections. The crucial newtechnical tool is a slice analysis in the Fr\'echet setting.

Yang-Mills moduli spaces over an orientable closed surface via Fr\'echet reduction