Differential Topology (Math 494/639)

A manifold is a topological space that locally looks "smooth", or like Euclidean space. For example, a beach ball or the surface of a donut are smooth manifolds, but an icecream cone is not.

In this course, we develop the theory of smooth maps between manifolds, intersection and transversality, the orientation of a manifold, and integration (calculus) on manifolds (including differential forms). Given enough time and ambition, we will discuss de Rham cohomology, group actions, and equivariant cohomology.

The requirements for the course are minimal: students must have taken MATH 315 (or equivalent) and MATH 322 (or equivalent).  It's recommended (but not required) that students have taken an introductory course in topology. Should you take this as an undergraduate or a graduate course?

Requrired Text: Differential Topology, by Guillemin and Pollack, published by Prentice-Hall
Recommended Additional Text: An Introduction to Differentiable Manifolds and Riemannian Geometry, by William Boothby, published by Academic Press