Cornell Math - MATH 652, Fall 2000

MATH 652 — Fall 2000
Differentiable Manifolds

This is an introduction to differential geometry and differential topology at the level of a beginning graduate student. Prerequisites are advanced calculus, linear algebra and point-set topology.

I intend to cover most of volume I of Spivak's Comprehensive Introduction to Differential Geometry. The main topics are smooth manifolds, embeddings, vector bundles, flows, foliations, differential forms, Stokes' theorem, de Rham cohomology.

Some of this material may have to be deferred to Math 653, which will be taught in the Spring and will cover topics such as connections, curvature, transversality, Morse theory.

I will ask the bookstore to order the textbook. It can also be obtained directly from the publisher at www.mathpop.com. The old edition (typewritten, but otherwise almost identical to the new) is available at a discount.