Prof C M Hull FRS
The course will use examples from mechanics, quantum theory, electromagnetism, general relativity and gauge theory to illustrate these ideas and their application in physics.
The idea of a manifold. Tangent vectors, vector fields and flows. Differential forms and exterior calculus. Differential forms and exterior calculus.
Integration, Stokes' Theorem and Cohomology
Integration of differential forms. Stokes' theorem. Cohomology and de Rham's theorem.
Volume forms and non-coordinate bases. The Hodge star. Connections, covariant differentiation, torsion and curvature. Cartan's structure equations.
The idea of a bundle. Vector and principle bundles.