Homotopy Invariance: Homology Groups

This lecture covers the concept of homotopy invariance and its application to homology groups of quotients, demonstrating how two continuous maps can be homotopic and the resulting isomorphism between homology groups. The instructor explains the decomposition of singular n-simplices into (n+1)-simplices and the prism-operators used in the process. The lecture concludes with a detailed proof of the homotopy invariance theorem, showcasing the chain homotopy and the resulting isomorphism. Various examples and illustrations are provided to aid in understanding the theoretical concepts.