Math 215b: Algebraic topology

UC Berkeley, Spring 2005


Michael Hutchings
[My last name with the last letter deleted]
Office phone: 510-642-4329.
Office: 923 Evans.
Office hours TBA.

Here are the term papers.

Spacetime coordinates

TTh, 8:10 AM, 31 Evans.

About the course

I assume you have learned the basics of algebraic topology, in 215a or elsewhere. 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. Where we start in 215b will depend in part on where 215a ends (which I will find out at the end of the fall semester). In any case, I expect to do something similar to last year's 215b course, in which we discussed the following topics:

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 official course requirement will be to write an expository paper, of about 10 pages, on some specific topic of interest in algebraic topology. Click here for more detailed guidelines. Inspired by Prof. Weinstein, I will also ask you to referee (i.e. make anonymous critical comments on) the paper of one of your classmates, and then revise your paper in light of the referee report you receive. Your final paper will (if you give permission) be posted here for your classmates to read.

Term paper deadlines:


You should already have a basic graduate level algebraic topology text. One of my favorites is Topology and Geometry by Bredon, in particular because of its emphasis on smooth manifolds.

The part of the course on bundles and characteristic classes will roughly follow the beautiful book Characteristic classes by Milnor and Stasheff. Other parts of the course will not follow any particular book, but I will give references for specific topics as we go along.

Lecture summaries

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