Differential Topology and Geometry with Applications to Physics

Differential geometry has encountered numerous applications in physics. More and more physical concepts considered as fundamental can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, general theory of relativity, string theory and gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can h...