The rational homology ring of the based loop space of the gauge groups   and the spaces of connections on a four-manifold
  We provide the rational-homotopic proof that the ranks of the homotopy groups of a simply connected four-manifold depend only on its second Betti number. We also consider the based loop spaces of the gauge groups and the spaces of connections of a simply connected four-manifold and, appealing to~\cite{TI} and using the models from the rational homotopy theory, we obtain the explicit formulas for their rational Pontrjagin homology rings. 
Svjetlana Terzic
math.AT