Cohomology and Integration

Abstract

The main emphasis in this monograph is on models of synthetic differential geometry, and it is not our purpose to give a systematic treatment of the synthetic theory. It seems nevertheless worthwhile to give some illustrations of synthetic differential geometry at work. Accordingly, the purpose of this chapter, and even more so of the next, is to actually develop some differential geometry in the synthetic context. The treatment is self-contained; in particular, the first three sections of this chapter do not presuppose familiarity with the corresponding classical theory. The models discussed in the previous chapter will play a crucial rôle when it comes to comparing the synthetic framework with the classical one.