Cornell Math - MATH 652, Fall 2003
MATH 652
Differentiable Manifolds I
(Fall 2003)
Instructor: Brian Smith
This is an introduction to differential geometry at the level of the beginning graduate student. The prerequisites are advanced calculus, linear algebra, and point set topology. The topics covered will include: topological manifolds, differentiable manifolds, immersions and embeddings, tangent bundles, fibre bundles, vector fields and dynamical systems, Frobenius' theorem, Lie groups, differential forms, integration on manifolds, Stokes theorem, connections, Riemannian manifolds, geodesics, curvature. The last four topics are also covered quite thoroughly in MATH 662 and so they will probably be discussed to a lesser extent than the other topics. As time permits, we will also cover as much Hodge theory as possible, and we may also have time to discuss additional topics as requested by the students.