A topologist's account of Yang-Mills theory (Q1201340)

The gauge theories are, perhaps, the most important modern domain of interaction between physics and mathematics. The purpose of this paper, excellent solved by the author, is to account for some essential problems in this field. There are presented the necessary notions and theorems from differential geometry field, like the principal bundles, bundle maps, connections, curvature forms, the Hodge star operator and others. Next, the Yang-Mills functional is defined. In order to study the instanton (an absolute minimum for the Yang-Mills functional), the Chern- Weil theory is presented. As a concrete example the magnetic monopole is considered. -- The bibliography contains 28 very rigorously selected references.