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

2016/03/26 by Svjetlana Terzić, Svjetlana Terzic, Terzic, Svjetlana
Computer Science · Mathematics · #55P35 (Primary) #55P62 #57R19 #81T13 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #msc:55P35 #msc:55P62 #msc:57R19 #msc:81T13

paper · pdf · doi:10.48550/arxiv.1603.08100

10 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

openalex publication_date 2016/03/26 · arxiv created 2017/01/16 · arxiv updated 2017/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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~\citeTI and using the models from the rational homotopy theory, we obtain the explicit formulas for their rational Pontrjagin homology rings.

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