Group Actions and Fundamental Groups

This lecture explores the concept of group actions on spaces, focusing on a cyclic group of order 2 acting on a graph. The instructor discusses the notion of totally discontinuous actions and their implications, leading to the identification of fundamental groups and homomorphisms. Through visual representations and examples, the lecture delves into the construction of coverings, identification of fundamental groups, and properties of induced homomorphisms. The discussion extends to free groups, generators, and relations, showcasing the richness and complexity of fundamental groups in various topological spaces.