Basic Algebraic Topology

Chapter 3 Covering Spaces and Fundamental Group

We shall now study one of the most basic concepts in algebraic topology, viz., the covering spaces. They are closely related to the study of fundamental groups on the one hand and to the study of the discontinuous groups on the other. Having met the notion of fundamental groups, it is time to study the theory of covering spaces and their relation with fundamental groups. We shall also study a little bit about the ‘discontinuous groups’, vis-a-vis covering spaces and fundamental group. Classically however, these concepts occurred in the reverse order. The study of discontinuous groups goes back to the time of Gauss and occurred in the theory of elliptic functions and then in the theory of modular ...