Summary
We'll try to cover Chapter 3 of Hatcher's notes,
including some appendices if we have time.
The grade is based on homework, a take-home final, and "participation".
Participation includes "scribe duties".
I'll scan the notes from the scribe and put them in
my cohomology folder at google docs.
Homework
- Due Jan 19: Questions 2,5,6,8 on p204-205.
- Due Feb 1: Questions 1,3,4,7 on p228-229.
- Due Feb 19: Questions 1,2,3,4 on p257.
Remarks
Here is my version of the universal coefficient theorem for cohomology.
Suppose you know the homology of a space X,
and you want to know the cohomology.
Figure out a chain complex, any chain complex,
that gives the right homology.
Proceed as if your made up chain complex
is in fact the simplicial (or singular or whatever) chain complex of X.
You will get the right answer.
This works because two chain complexes have the same homology
if and only if they are chain homotopy equivalent
(so "basically the same" for our purposes).
I don't know a good reference for this fact,
but here is a link to where
I asked it on mathoverflow.
Prof. Bigelow
2009-09-27