A primer on computational group homology and cohomology

David Joyner

Published 2007-06-04, updated 2009-06-10Version 2

These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You should know the definition of a (left) module over a (non-commutative) ring, what $\zzz[G]$ is (where $G$ is a group written multiplicatively and $\zzz$ denotes the integers), and some ring theory and group theory. However, an attempt has been made to (a) keep the presentation as simple as possible, (b) either provide an explicit reference of proof of everything. Several computer algebra packages are used to illustrate the computations, though for various reasons we have focused on the free, open source packages such as GAP and SAGE.