A manifold is a topological space which looks locally like , but not necessarily so globally. By introducing a chart, we give a local Euclidean structure to a manifold, which enables us to use the conventional calculus of several variables. A fibre bundle is, so to speak, a topological space which looks locally like a direct product of two topological spaces. Many theories in physics, such as general relativity and gauge theories, are described naturally in terms of fibre bundles.
Relevant references are Choquet-Bruhat et al (1982), Eguchi et al (1980) and Nash and Sen (1983). A complete analysis is found in Kobayashi and Nomizu (1963, 1969) and Steenrod (1951).
Problems
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