Math 141: Differential Topology


Essential Prerequisites:
Students should be very comfortable with the following concepts:
i. Continuity of functions (from R^n to R^n, and on general metric spaces)
ii. Metric spaces
iii. Topology: open and closed sets, compactness, covers, homeomorphisms.
iv. Multivariable calculus: Differentiability of functions from R^n to R^n. Linear maps.

Suggested reading for i-iii: A. Hatcher's Notes on introductory point-set topology or Chapter 2 of C. Pugh's book Real Mathematical Analysis.

General information for students


The textbook for this course is Differential Topology by Guillemin and Pollack. We will cover most of chapters 1, 2 and 3.

Supplementary reading (not required)

- Chapter 1 (two lectures on manifolds) from A mathematical gift III. Highly recommended as motivation for the content of this class.
- L. Christine Kinsey, Topology of Surfaces (alternate text suggested by a previous instructor)
- V. V. Prasolov, Intuitive topology. (not as closely related to this class, but a good perspective on aspects of topology)

Also of interest

You may enjoy doing an independent study through the Directed Reading Program .

Problem sets and reading

image credit: the illustration of topology at the top of the page is by Robert Ghrist