Chapter 16 - Differential Graded Algebras in Topology

Abstract

This chapter discusses the differential graded algebras in topology. The homotopy theory of topological spaces attempts to classify weak homotopy types of spaces and homotopy classes of maps. For a given geometric problem, however, it is often sufficient to replace the homotopy theory of spaces by a weaker “algebraic” homotopy theory as described, for instance, in Baues' book. This chapter considers the specific case when spaces are modeled by the homotopy theory of differential graded algebras.