The rational homology ring of the based loop space of the gauge groups and the spaces of connections on a four-manifold

Abstract

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.

arXiv comment10 pages, some typos corrected, to appear in the volume of Fundamentalnaya i Prikladnaya Matematika honoring Yuri Petrovich Solovyov (in Russian); English translation in Journal of Mathematical Sciences