Math 215b: Algebraic topology

UC Berkeley, Spring 2004

This course is over. Some of the student term papers are available here.


Michael Hutchings
[My last name with the last letter deleted]
Office phone: 510-642-4329.
Office: 923 Evans.
Office hours: by appointment for now; I may pick a regular time a little later.

Spacetime coordinates

As of 2/12, we are moving to 41 Evans. (The old room was 65 Evans.) The time is TTh, 11:00 - 12:30.

About the course

In 215a we studied the fundamental group, homology, and cohomology, from Chapters 1-3 of Hatcher's book "Algebraic Topology". (We skipped over some of what Hatcher did, and we did a few things which Hatcher didn't, particularly in connection with differential topology. Bredon's book "Topology and Geometry" is a good reference for those additional topics.)

With the basics of algebraic topology established, in 215b we will study a selection of more advanced topics, which nonetheless are in my opinion very important and useful in geometry and topology. I will emphasize applications to the geometry of smooth manifolds. We will do as much of the following as time permits (not in exactly this order):


You should already have a basic graduate level algebraic topology text such as Hatcher and/or Bredon; this will help with the first part of the course. The beautiful book "Characteristic classes" by Milnor and Stasheff is strongly recommended reading for a substantial part of the course. "Differential forms in algebraic topology" by Bott and Tu gives a very nice exposition relating to some of the topics in the course. I will give more references for specific topics we cover as the course progresses.

Course requirements

I will suggest some homework exercises; these will not be graded, although I am happy to discuss how to solve them.

The only course requirement will be to write an expository paper on some specific topic of interest in algebraic topology. This should be about 10 pages or less. Inspired by Prof. Weinstein, I will ask students to anonymously referee each other's papers and then revise them. Click here for more details.

Lecture summaries

Summaries of the lectures with references as appropriate will be posted here.
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