Peter Teichner
Math 253, Homological Algebra
Spring 2008, Tu/Th 11-12:30 in 3 Le Conte
Office hour Tuesday 2-3 in 703 Evans.
GSR: Chris Schommer-Pries, office hour Wednesday 9-10 in 1060, discussion session Friday 12-1 in 939 Evans.
Please submit the first problem of the following sets in writing, other problems will be discussed during the Friday 12-1 session.
Homework 1 , due Friday, Feb. 1
Homework 2 , due Friday, Feb. 8
Homework 3 , due Friday, Feb. 15
Homework 4 , due Friday, Feb. 22
Homework 5 , due Friday, Feb. 29
In each group, please submit different problems in writing during the following weeks.
Homework 6 , due Friday, March 7
Homework 7 , due Friday, March 14
Homework 8 , due Friday, March 21
Homework 9 , due Friday, April 4
Homework 10 , due Friday, April 11
Homework 11 , due Friday, April 18
Homework 12 , due Friday, April 25
Homework 13 , due Friday, May 2
The class will start with basic constructions for chain complexes, with an eye towards group cohomology. We'll explain the relation of the first three cohomology groups with extensions of groups and we'll show how group cohomology drastically restricts the class of finite groups that can act freely on spheres. The second part of the class will introduce spectral sequences, a basic tool in all computational aspects of cohomology theory. In the last part of the class we'll study some homotopical algebra, including derived categories and their application.
The best way to learn the material in this course is by doing your own diagram chases and
guessing your own definitions. That's why we'll have homework problems every week, posted on this website. They will be partially due in writing and partially presented during the discussion hour with Chris.
Recommended Reading:
Brown, Cohomology of groups
Cartan-Eilenberg, Homological algebra
Gelfand-Manin, Methods of homological algebra
MacLane, Homological Algebra
Weibel, Introduction to homological algebra