Cornell Math - MATH 740, Spring 1999

MATH 740 — Spring 1999
Homological Algebra

Instructor: Allen Hatcher

Time:  MWF 12:20-1:10

Room: WE 328

The subject of homological algebra grew out of algebraic topology but has developed a life of its own, and now its influence can be felt in many areas of modern mathematics. This course is intended to be a broad introduction to the subject. There is a rather nice recent book by Charles Weibel called "An Introduction to Homological Algebra" which will serve as a sort of textbook for the course. The book's table of contents gives some idea of the topics:

Chain Complexes/ Derived Functors/ Tor and Ext/ Homological Dimension/ Spectral Sequences/ Group Cohomology and Cohomology/ Lie Algebra Homology and Cohomology/ Simplicial Methods in Homological Algebra/ Hochschild and Cyclic Homology/ The Derived Category/ Category Theory Language

Naturally we won't be able to cover the whole book in a semester but will omit some of the more advanced topics.The main prerequisite for the course is familiarity with basic abstract algebra, as in our first semester graduate course 631. Prior knowledge of algebraic topology is not assumed, but connections with topology will be sketched when appropriate.