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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 a 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, using the models from rational homotopy theory, we obtain explicit formulas for their rational Pontryagin homology rings.

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Correspondence to S. Terzić.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 6, pp. 205–215, 2016.

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Terzić, S. The Rational Homology Ring of the Based Loop Space of the Gauge Groups and the Spaces of Connections on a Four-Manifold. J Math Sci 248, 803–809 (2020). https://doi.org/10.1007/s10958-020-04914-x

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