Suppose G is a group, and X is a path-connected topological space whose fundamental group is G and whose higher homotopy groups are trivial. Then X is unique up to (weak) homotopy type and so its cohomology is an invariant of the group G, called the cohomology of G. These cohomology groups can also be defined algebraically; this was the beginning of homological algebra. Apart from being an interesting invariant of the group G, the notion of group cohomology plays an important role in algebraic number theory, algebraic geomoetry, and algebraic topology. This course is an introduction to the subject. We will begin by defining and studying the basic properties of group cohomology; later topics will probably depend upon the interests and background of the audience. One possibility is to study how the mod(p) cohomology of a finite group is related to the cohomology of its elementary abelian p-subgroups.

Prerequisites: the first year algebra sequence and some knowledge of algebraic topology, although this last requirement may not be essential. Interested students should discuss their background with me.