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.
A number of homework exercises will be handed out over the course of the term. These will form the basis of the final grade for anyone registered in this course.
Here follows an overambitious list of topics.