Characteristic Classes

Abstract

We have had a number of previous, albeit informal encounters with the notion of a characteristic class for a principal bundle (in Section 2.2, 2.4 and 2.5) and are now in possession of sufficient machinery to take up the subject in earnest. Before plunging into the thick of the battle, however, we would like to make clear the strategy we propose to adopt. This is perhaps best achieved by going through what might be regarded as the “trivial” case in detail and then indicating the modifications required when matters are not so simple.