Fibre Bundles. General Theory

Abstract

The notion of locally trivial fibre bundle naturally generalizes that of the manifold. The theory of these bundles was developed in fifties especially by Ch. Ehresmann but its origins are found in the works of E, Cartan. The fibre bundles were used to get global results in differential geometry as well as to build geometrical models for modern physical theories. As one of the our main purposes is to describe such geometrical models, it is natural to begin with a recalling of the main notions and results from the theory of the fibre bundles. This is the object of the first chapter.