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

Svjetlana Terzic

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arXiv · 1603.08100

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

Svjetlana Terzic

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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.

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Svjetlana Terzic. 2016-03-26. The rational homology ring of the based loop space of the gauge groups and the spaces of connections on a four-manifold. https://arxiv.org/abs/1603.08100

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