Group Actions: Quotients and Homomorphisms

This lecture explores group actions, quotients, and homomorphisms, focusing on the practical implications for various groups, such as circles and spheres. The instructor discusses the concept of attaching cells to describe complex projective spaces, emphasizing the construction process and comparisons between different constructions. The lecture delves into the injectivity and surjectivity of mappings, demonstrating how to establish bijections between compact and separated spaces. Additionally, the lecture touches on the notion of exact sequences in the context of cell attachments and provides insights into the connections with homotopy, fibrations, and cofibrations.