Course Schedule and Catalog

Long Title: TOPOLOGY OF MANIFOLDS

Department: Mathematics

Grade Mode: Standard Letter

Language of Instruction: Taught in English

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): (MATH 444 OR MATH 539) AND (MATH 445 OR MATH 540)

Description: A graduate course on the topology of fiber bundles, especially vector bundles and principal bundles, as well as their characteristic classes. It will cover differential forms as well as Stiefel-Whitney, Euler, Chern, and Pontryagin classes. If time allows, other topics may be included. The prerequisites for the class are the material from Math 444/539 and Math 445/540. In particular, the student should be familiar with smooth manifolds, the tangent spaces, homotopy groups, covering spaces, and homology groups.