Klimek-Chudy, Sławomir; Kondracki, Witold III The topology of the Yang-Mills theory over torus. (English) Zbl 0575.58012 Suppl. Rend. Circ. Mat. Palermo, II. Ser. 6, 161-175 (1984). With the physical motivation of cut-offs for Yang-Mills theory, the authors study the topology of principal bundles over a three-torus. Their main results are that isomorphism classes of principal G-bundles over \(T^ 3\), with G a compact, connected Lie group are labelled by \(\pi_ 1(G)\times \pi_ 1(G)\times \pi_ 1(G)\) and that the homotopy class of an automorphism of a principal G-bundle is determined by an element of \(\pi_ 1(G)\times \pi_ 1(G)\times \pi_ 1(G)\times \pi_ 3(G)\). This latter result gives the fundamental group of the moduli space of connections modulo gauge transformations which are the identity at a point. The method is an inductive use of the theorem of Steenrod that the isomorphism class of a principal bundle on \(M\times S^ 1\) is determined by a principal bundle on M and the homotopy class of an automorphism. Reviewer: N.Hitchin Cited in 1 Document MSC: 58D30 Applications of manifolds of mappings to the sciences 57R22 Topology of vector bundles and fiber bundles 81T08 Constructive quantum field theory 53C80 Applications of global differential geometry to the sciences Keywords:Yang-Mills theory; principal bundles; principal G-bundles; gauge transformations; automorphism PDFBibTeX XMLCite \textit{S. Klimek-Chudy} and \textit{W. Kondracki III}, Suppl. Rend. Circ. Mat. Palermo (2) 6, 161--175 (1984; Zbl 0575.58012)