Introduction

Abstract

This chapter is an informal introduction to the material in the rest of this book. The goal of the book is to relate smooth differential forms of a manifold to classical algebra-topological invariants. The next seven chapters are a review of the basics of classical homotopy theory including the Postnikov tower of a space and the localization of a homotopy type at 0, forming its rational homotopy type. Chapters 9–15 introduce differential forms and their homotopy theory of differential graded algebras and relate these notions to those of rational homotopy theory as introduced in Chaps. 2–8.