Math 214: Differentiable manifolds

UC Berkeley, Spring 2015


Michael Hutchings. [My last name with the last letter removed] Tentative office hours: Thursday, 10:00-11:30, 2:00-3:30, 923 Evans.


The official textbook for the course is John Lee, Introduction to smooth manifolds, second edition. (The first edition presents the material in a different order and omits some key topics such as Sard's theorem.) The following are some other books which I recommend, in order of increasing difficulty. These are classics; I read all of them (except Munkres) when I was a student and really enjoyed them.


The basic plan is to cover most of the material in chapters 1-19 of Lee's book (adding a few interesting things which are not in the book, and some bits from chapters 20 and 21). My goal is for you to understand the basic concepts listed below and to be able to work with them. This material is all essential background for graduate level geometry (except possibly for the most algebraic kind). In class I will try to introduce the main ideas, explain where they come from, and demonstrate how to use them. I will tend to leave technical lemmas for you to read in Lee's book (or not).


The course grade will be based on homework, which will be due at the beginning of class on Tuesdays. (There might be no homework on occasional weeks if we have not covered enough material for a new assignment.) Homework will be peer-graded. Collaboration on homework is encouraged but must be acknowledged.

What we actually did in class