Math 215b Final project

The only official requirement for this course is to write an expository paper, of about 10 pages, on some topic of interest in algebraic topology or a closely related field; to "referee" (i.e. make anonymous critical comments on) the paper of one of your classmates; and then to revise your paper in light of the referee report you will receive. I suggest the following schedule:

The topic should be fairly specific; it is better to understand a small area in detail and be able to prove at least something. However it is also good to indicate how the topic is connected to other things. You can do pretty much anything you want. For example, here are some topics which people already told me that they want to do (although there is no reason why two people can't write about similar things, and also your topic can be a little less advanced than some of these): There are many interesting topics in the sections of Milnor and Stasheff, Hatcher, or Bott and Tu that we did not cover in class, so you might want to learn about one of these (probably looking at other sources as well in order to go into more depth). For topology up to 1960, a neat book is "A history of algebraic and differential topology 1900-1960" by Dieudonne, which summarizes an amazing amount of material while still indicating the mathematical ideas. (However the older papers referenced in this book might be hard to read so you may want to find modern treatments.) It might also be fun to learn about more recent developments. Low-dimensional topology (i.e. topology of manifolds of dimension 4 or less) is currently extremely active, with many fascinating topics you can start to learn about; I can help you pick out something. (This is what i actually do research in.)
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