There is no general textbook reference for this course, but references will be given over the course of the term for specific aspects. Notes may also be made available.
This is a topics course in the homotopy theory of classifying spaces of groups, and related aspects of homotopy theory. We have three principal aims: first, to explain how (algebraic) group cohomology for discrete groups can be viewed a special case of a homotopy-theoretic study of classifying spaces; second, to give an introduction to the theory of G bundles and characteristic classes; and third, to establish computational tools which are more generally applicable.
A first course in algebraic topology (such as Math 527) will be assumed.
Exercises for this course can be found here. Please submit the answers to 5 questions to me on or before 14 December in order to receive a course grade. The list of exercises may be expanded as the course progresses.
Here follows an overambitious list of topics.