Items list
Description
Definition of differential (smooth) manifold, examples (Rn, Sn, GlnR), quotient manifolds (RPn), differentiable functions, tangent vectors and tangent space, smooth mapping differential, submanifolds, immersions, subimmersions, the constant order theorem, applications to matrix groups O(n), U(n), Sp(n), the tangent bundle, vector bundles, partitions of the unit, bulge functions, vector fields, Lie product, integral curves, elements of Lie groups, closed Lie subgroups, the Lie algebra of a Lie group, left invariant vector fields, the conjugate representation, differential forms on manifolds, cotangent space, cotangent bundle, invariant forms on Lie groups, exterior derivative, manifolds with boundary, integration on manifolds, Stokes' Theorem.
